Are you talking resort skiing or backcountry (if I'm at a resort I like to try and eat on the lifts to maximize my shreddin' time)?
For backcountry: I usually bring a little plastic tupperware dish with some chicken salad or tuna salad, a couple packets of almond butter, and a piece of fruit or two. I also have a few Kind bars and Larabars on hand just in case I end up spending more time out there than I plan ... though these things are painful to eat when cold so if I'm going to eat one I usually throw it in an inside pocket for 15 minutes so my body heat can soften it a bit.
For resorts: cabbage wraps ... they're like a sandwich, but the meat/cheese is wrapped in a cabbage leaf instead of bread. You can eat these on the lift depending on how long of a lift ride it is. Also clementines (those little oranges that peel really easy) are good too.
That's about all I got ... if it's a powder day and I don't have food I'll usually end up doing an impromptu IF so I can maximize time on the slopes
As to the second question, if it's a ski-mountaineering trip, you wouldn't need a fridge ... I've found that things like butter and cheese keep pretty well for a few days in a moderately cold environment.