The same cities are not thought of as capable of hosting both Summer and Winter Olympics. You need gigantic urban centers for the Summer Games, and Winter Games require state-of-the-art ski resort towns or large cities next to mountain ranges. There are a few that might be possible in theory- Munich, 1972's summer host, made a bid for the 2018 Winter Olympics, but lost out- so never say never, but there aren't many that can have that kind of dream.
Although there is one city that doesn't have to dream, because it's already done it.
The host city can't host every single event on its own. Some events get farmed out to satellite towns around the general area- sailing gets farmed out to a coastal town, canoe/kayak and rowing needs a town with a still or manmade lake and possibly a river location as well, soccer needs multiple venues and is shared with several cities around the host nation, mountain biking and BMX need some fairly hilly terrain and/or parkland, skiing needs a mountain, biathlon and cross-country skiing needs rural, semi-hilly-but-traversable terrain with some kind of trail, and then there are the various suburbs and outlying towns that manage to score random events that end up falling outside the main competition complex.
Karuizawa, Japan is one such satellite town. When Tokyo hosted the Summer Games in 1964, Karuizawa, a get-away-from-it-all town for residents of Tokyo, was called upon to host the equestrian events. The town sits in Nagano Prefecture, so when Nagano won hosting duties for the Winter Olympics in 1998, Karuizawa was in position to be a satellite town again, and they were given the curling competition. To date, they're the only city that's seen competition in both Olympic seasons.
At least until Munich bids again, that is.