What shoes have you used in the past and liked? That might help steer you towards a new pair.
I think I have had 3-4 INOV8 trail running shoes and I bought every pair of a certain road model I could find. The Trailroc series was pretty cool for trail running. I would say the Altra Superior is pretty close to those now. Anyhow, there was not much difference between their men’s and women’s shoes a few years back. You’re right about the M and U in the model names/numbers and just ordering the equivalent size in the other gender…as far as a few years ago. The boxes for my road x lites had both the men’s and women’s size listed. I’m not sure why it would have changed now, but I suppose there’s a chance they have. I don’t remember if the trail shoes had both sizes listed. There were very clearly M and W models for those, while the road stuff was U. Happyscientist made a good point about widths sometimes being different between men’s and women’s.
The thread quickly turned into a Solomon advertisement instead of answering Q1. The Solomons recommended above are pretty cool and can handle most winter running conditions. Too much heel-to-toe drop and narrow for me. There’s also a pretty wild S-Labs version one of my friends is loving this winter here on the IL/WI border. If you’re planning on running on groomed or packed down surfaces, they might be more shoe than you need. I have been pretty happy with the Altra Lone Peak Neoshell this winter. Aggressive enough lugs for most things, waterproof (except the tongue) so the feet stay dry when it’s melty, and a bit more padded which I like when there’s hard ice spots or rocks/roots hidden under snow. There’s a mid-top version as well. There’s also an Altra specific gaiter that I like better than the traditional loop around the shoe type gaiters.