Edinburgh in late March

My daughter and I went to Edinburgh for a week this last March, we were there early in the month.

It was cold, as it's very humid in Scotland. I'm from Colorado, so I was prepared clothing wise.

We had no rain, and even had sunny days, but cold temps..probably 30 but warmed up to almost 50 a couple of days.

If you layer well, and wear a hat/gloves/scarf or BUFF, you should be OK. I wore a long down jacket (that I got at Costco) with a wool sweater and my jeans. I had waterproof booties. My daughter got by in a fleece jacket and a down vest over that. (I tend to run colder than she)

For the kids, the walk up to Calton Hill offers great views and isn't difficult. The cemetery on the way up the steps is interesting. Take a ghost tour at night, explore the closes... of course visit the Castle. The Tartan mill just below the castle is a fun place to spend an hour or so out of the cold. It's mostly shopping, but there is also a fun exhibit of the history of the tartan , and it's great to watch the making of tartan in the lower level.

One thing I regret is not making it to Dean Village...maybe on the next trip..

I'd highly recommend spending the money (honestly, they aren't expensive for what you get) and taking a full day Rabbie's tour. you can choose to see castles, or some Highland Lochs, Hadrian's Wall, or get up to Stirling Castle and drive through Loch Lomand National Park to see the Highlands of Scotland. They drive you around, but also let you out to stretch your legs, and there is always a guide explaining the history of what you are seeing.

Thank you soo much for all your tips =)

For clothing, the watchwords are layers, waterproofing, lightweight, and low bulk. Silk camisoles/undershirts (Wintersilks), a cashmere sweater (try Goodwill or look for sales online), rain hat, fingerless gloves, socks & boots. Look for warm socks such as Smartwool (dries faster than regular wool -- do NOT bring cotton socks as they take forever to dry). Hammacher Schlemmer also sells quick-drying travel socks but they're expensive. Outerwear, I brought a trench coat with removable liner.

To give you an idea of the layering-up experience unfamiliar to SoCal residents, in Scotland in May I usually wore my trench coat with the liner in, with a wool blazer under that, a cashmere sweater under that, an alpaca scarf at the neck, and a silk camisole under that.

For footwear, I did well with low-heeled leather fashion boots that can go over jeans in daytime and go with tights and a dress in the evening. My only other footwear was a pair of roll-up slippers like FitKicks or similar, to slip into at the hotel & give my feet a break from the boots.

Weather will probably be wet. Spray all outwear liberally with waterproofing before you leave home: Scotchgard for clothing, silicone spray for footwear and especially be sure to thoroughly treat the area where the sole meets the upper.

If you want to get in out of the weather, the National Museum is spacious & airy and has a wide variety of fascinating exhibits for all ages. Another indoor activity that the kids might really enjoy is the tour of Mary King's Close; see https://www.realmarykingsclose.com/

Weather,in Scotland we have a saying about March weather, In like a Lion out like a Lamb or in like a Lamb and out like a Lion, so it could be really nice or really terrible you just never know.
Additional things to do for the kids in addition to what's been mentioned .Our Dynamic Earth, good for a real bad day.
Also 2 museums on the Royal Mile (Cannongate area) The People's Story and the Edinburgh Museum both small museums but very interesting and the buildings they are in are quite lovely, they are also free.
There is a Museum of Childhood on the High street part of the Royal Mile, but this is closed for refurbishment and I am not sure when it will reopen