Scotland in October (or England? We have options!)

Why not make a wish list of "I'd like to see's" and see what falls out of that? You could end up with a route, or a long stay in London and Edinburgh. Will you rent a car? Much easier to explore and "see" either the English or Scottish countryside.

Early October shouldn't be a bad time for either location. Google average temps and rain fall for the locations and dates you are interested in.

I don't think anyone can tell you which is best - very much a personal decision. As one who has toured both rather extensively, I doubt that you will be disappointed with either choice as long it is based on your personal interests.

October weather can be very variable. You could get wet and windy weather but you could equally have lovely Autumnal days. Quite likely a bit of both. The beginning of October should still be pretty OK.
You can easily fill ally out time in Scotland. As well as the abundance of beautiful countryside you will find lots to entertain you in both Edinburgh and Glasgow. I’m writing this from Glasgow, where I’m visiting for the World Cycling Championships and I am reminded what a wonderful city it is - I would argue at least if not more impressive than it’s rather more hyped neighbour Edinburgh, although in a very different way.
You could also dip into Northern England if you wish for more wonderful countryside in Northumbria and the Lake District. I can’t however see the point in travelling all the way south to see what in my opinion is the wildly over-hyped Cotswolds. You would be travelling past many many better areas to get there.

It sounds like you've gotten unreasonably worried about bad weather. You're very unlikely to have ice & snow in October. It will likely rain part of the time, but that's true in spring and summer as well as autumn. Dress in layers, especially warm wool layers and waterproof outerwear.

Because the days are relatively short in October, I would plan more city time where you have indoor options (museums, castles, churches). Don't risk getting caught out hiking after dark.

Personally although I love England, with only 10 days and your flight in/out of Edinburgh, I would stay in Scotland. There is plenty to see and do without taking many hours of travel time down to the Cotswolds and back. But of course it's up to you -- the main thing is to enjoy a "just the two of us" getaway, right?

I was in Scotland and had a ball. Since your flights are into and out of Scotland, I would spend my precious vacation time in Scotland.

I agree with Kim and epltd. Spend all your time in Scotland. We were there in June, and the scenery is beautiful and will take your breath away. We loved every place we visited but we agree that Skye and Glen Coe are the two most beautiful of all the places we visited. If you don't have time to drive to Skye and if the weather there is too iffy, then definitely spend a couple nights in Glen Coe. Drive down the Glen Etive Road. Just beautiful!

We had 4 nights in Edinburgh and we wish we had 5 nights. As someone else suggests, you can also visit Glasgow. The Fife Coast, not too far from Edinburgh, is lovely, too. Another place we stayed is Nairn, a seaside village about 30 minutes from Inverness. Include some castles in your itinerary. They would be great to visit if you have some rainy days. And sunny days, too!

I'm splitting 10 nights between York and Edinburgh. That might work for you if you want to visit England but not venture too far from where you'll fly out.