We are planning to fly into London on 12/24, spend 4 days there, then take the train to Edinburgh to explore the north 12/30-1/2. We would like to see Edingburgh, but aren't sure we're interested in all the Hogamanay festivities. We are interested in renting a car to see the country-side. My questions are: 1. are we really missing something if we avoid Edinburgh on the 31st/1st (the torches parade does look fun)? 2. Are we likely to run into treacherous driving outside the cities in winter? 3. Where would you go and/or avoid? Isle of Skye looks wonderful, but so does the North Lake District (not actually Scotland, but wow)? Glasgow also looks wonderful... St. Andrews? Oh and we are a family of 4, including two teenagers (15 & 18).
You only have three days (arrive 12/30, leave 1/2), is that right? You could easily find fun and interesting things to see and do in Edinburgh for that length of time, so you really would not need to rent a car.
OTOH, if you're more interested in the countryside than city, you could either drive or take the train to another location. Days are very short at that time of year and personally I wouldn't want to be driving in the dark on Scotland's rural roads, even if icy conditions were not likely. The higher the altitude the greater risk of ice. Scotland has an excellent network of buses serving the more rural areas, but again I'd be nervous about icy roads.
A big caveat for your specific time period is holiday closures, because two of your four days are bank holidays (1/1, and 1/2), and -- as you noted -- 12/31 is a Scottish traditional holiday. I'm hoping someone else on this forum will have firsthand experience to advise about what's open on those days so you won't have to look up everything piecemeal.
First of all a reality check - it is roughly an 8 hour drive from Edinburgh to Skye. Daylight will be in short supply. There are no indoor sights (Dunvegan Castle closes in the winter) so you will be driving and then presumably hiking around in what is likely to be very cold, wet and windy weather. The Lake District is around a 4.5 hour drive from Edinburgh depending on exactly where you want to go in that area. Personally I would stick much closer to Edinburgh. How about Stirling - excellent castle, or Dundee with it's newly opened V&A art and design museum and the ship that Captain Scott sailed to Antarctica in.
Some attractions are likely to be closed over the New Year period, so you'll need to check carefully in advance.
You won't need a car in Edinburgh city centre, so if you do decide to take trips out of the city, I'd rent a car at the airport just for the day(s) you need it.
I don't think the Scottish countryside is likely to be very inviting between Dec 30th and Jan 2. This is a time to stay in the city, especially with such impressive Hogmanay traditions. (The days are very short indeed, look up on a weather almanac site to see how long the "sun" is up -- add to that the possibility of gray overcast days and that day gets even shorter.)
As SkyeGirl mentioned, a trip up to Dundee on the train to see the new V&A could fit the bill. But I wouldn't be crossing the country at that time to go to Skye and back, you'd spend your entire two full days on the 31st and 1st in the car, and largely in the dark.
Something worth considering would be the fireball march up in Stonehaven. It's on New Year's Eve, and starts at midnight, although you need to get there earlier to get a good spot. I think that there are some videos on the internet. Your teenagers would especially love it, unless there is a particular band they'd like to see at one of the many Hogmanay celebrations around Scotland. Trains run directly from Edinburgh to Stonehaven, if you don't fancy driving, and you definitely need to make accommodation arrangements in Stonehaven or Aberdeen.
I've only been to one Hogmanay celebration in Scotland. It was for the Millennium, and my favorite band, Runrig, was playing at Bught Park in Inverness, with MacUmba as an opening act. It was actually not too cold that night, and as just about everything (except for Blockbuster and a few pubs) was closed on New Year's Day (National Recovery Day), we drove out to Ullapool in brilliant sunshine.
We encountered no snow or black ice in ten days driving around Scotland during the changing of the centuries, but that doesn't mean to say that you won't. As everyone else has pointed out, four days (or less) is really not enough time to drive to and appreciate Skye in limited daylight. You'd be better served staying east and south of the Great Glen, and saving Skye and the Highlands for a longer holiday. You're only going to have about seven hours max of daylight at that time of year, and of that, only about five to six hours will be broad daylight. So you'll need to make the most of the daylight hours, and have activities planned for the evenings (which start around 3:30 p.m.).
Best wishes, and may I be the first to wish you a Happy Hogmanay!
p.s.: If you don't fancy partying with half a million people, avoid Edinburgh on New Year's Eve.
I attended the Hogmanay festivities in 2008 while in college. I thought that the Torch Light procession was worth the time. It is pretty amazing to see a river of torches along the Royal Mile. I also went to the street party which I didn't think was worth standing out in the cold for. There were a lot of inebriated teenagers and long lines.
As far as where to go, I would stay near Edinburgh (IMO). There are plenty of things to see and do in the city. Skye is a long ways away as other posters have said. St. Andrews makes for a good day trip especially if you like golf. Even if you are not into golf, it is a pretty little town to visit. Stirling isn't too far away and also makes a good day trip. There is an interesting castle there and a beautiful statue of Mel Gibson from Braveheart.
The Wallace/Gibson statue was moved to Ardrossan in Ayrshire last year. Apparently the 10 year agreement between the sculptor and the custodians of the Wallace Monument had ended. The sculptor had downsized his studio in Brechin, and didn't have room to store the statue. Wallace supposedly defeated the English garrison at Ardrossan Castle in 1298.
I don't know what the sculptor was thinking when he sculpted Wallace's/Gibson's mouth. It looks like one of those blow-up dolls.
I see that you mention that you are arriving in London on Christmas Eve.
Have you read the threads here about Christmas in London? Short version: you may want to organise the meals you will have on Christmas Day. London pretty much shuts up tight as a drum on Christmas, including zero Underground (Tube) trains and virtually zero buses. Taxis will charge the earth. Best to be within walking distance of your digs.
Transportation shuts down early on Christmas Eve. Trains are pretty much shut down from Christmas Eve early evening through Boxing Day. On Boxing Day most attractions and most stores (except some of those with sales) will be shut. Throughout the country, trains take the week between Christmas and New Years to do heavy maintenance and construction work. Expect many routes to be on diversion or closed. Check very carefully.
You ask about the weather. The truth is - nobody knows. It is often ok in parts of the country and diabolical in others. The worst storms tend to come in January and February, but a storm in December is by no means unheard of. A winter storm can have very high winds causing damage to trees, sometimes snow, sometimes ice. If you are driving across the Pennines you can almost be guaranteed bad weather much of the time.
Days will be short in London and the south and central parts of England, but not as short as in Scotland. I live in the Midlands and people often have their headlights on in the morning until 9 or so, and headlights often come on in the afternoon around 2.30 or 3, with complete dark by 4.
You can plan around all these, but you do need to plan.
25th and 26th December and 1st January are public holidays with 2nd January also a public holiday in Scotland.
Public museums if not closed for the season will be closed on those four days and public transport limited. In terms of accomodation this is not a time of the year I would approach without everything booked.
In terms of driving, the weather can and will be against you, there is very little day light that week and on the holidays most filling stations will be closed. If restaurants are open they will have been booked months in advance and will charge a premium.