Heriot Watt is a great university! I'm in my second year now, and although I'm not an acturial student, some of my friends are, and they seem to be enjoying it! All of the maths kids seem to have a tight bond with each other. And I haven't heard them make any complaints about the lecturers, except for physics?
I love the fact that is it a campus university, there are halls for first years which is so handy. Getting up 5 minutes before a lecture starts, fantasitic!
I live in town this year, and it can be a bit of a pain in the mornings but the buses come every ten minutes so its good.
The city of Edinburgh is amazing! especially at the moment with the winter wonderland! And you can usually find a student night any night of the week, cheap entry and cheap drinks! :P
And as for the weather, its in Scotland, what do you expect! Although i remember getting extremly sunburnt last year sitting out by the loch, and it is currently warmer, and less icey in edinburgh than it is in my hometown in the north of england.
I think the university in (wrongly) looked down upon by Edinburgh University, generally because they were there first and therefore more established, presticious. Most of my friends have never even heard of Heriot-Watt!
However, all this advice is extemely biast, as I love the place! So your best coming up and seeing the place for yourself before you make any big decisions.
Its easy enough to get to edinburgh from London, trains run pretty regular and take about 4/5 hours, but theres also plenty of cheap flights up as well. (It's about a tenner for a taxi from the airport to campus and takes 15 minutes max!)
PM me if you need any more advice