From New England where you have to shovel yourself out and get into work anyways so I appreciate that we rarely get snow in winter where I am in the UK, and when it does happen, it's almost always just a light dusting.
That being said, I MUCH prefer the warm. For me, it's less about the cold itself, but the cold accompanied by darkness when I leave the office at 5:15PM and dampness. I wouldn't mind it if I worked from home all the time and could choose when I wanted to go out into it, but I have a dog so can't just decide I don't want to walk her on a given morning/evening when it's exceptionally cold. The daily pains, IMO, aren't exactly miles away from what I dealt with in the US (E.G. defrosting the car/scraping the car off in the morning) minus the snow problem....but other parts of the UK will have to deal with snow far more than I would.
Can I tolerate the winters here? Sure. Do I actively enjoy them?: Nope. I almost definitely have SAD, so the brighter it is, the happier and more positive I will be and the warmer it is, the more I want to leave my house (which, again, has an impact on my mental health). I don't think it's necessarily down to location, however. I think some people are winter people and some people just aren't. Even back in the US, I absolutely hated when it would snow because it meant I had to go out into the freezing weather and shovel for what felt like ages. Some people love the cold and don't mind that but I would dread it. The less amount of time I needed to give in the morning before going to work, the better. While I enjoy some aspects of winter, I am just not a winter person regardless of where I'm located. (Sorry for the ramble, I've not finished my coffee yet so my brain isn't awake).