I think a successful winter without an indoor is primarily based of adjusting your expectations and approaching the season with flexibility in mind.
I live in northern CO without an indoor. For the last couple of winters, the wind is more of a hindrance than cold or snow, although the last couple winters have been on the mild side. It’s also almost always sunny here, and the sun is warm, which keeps the arena more thawed than it would be otherwise.
I work from home, so I have the flexibility to ride during the daylight hours. If you don’t have that flexibility and your outdoor isn’t lighted, you’ll want to plan on either finding another barn to board at for the winter or only riding on the weekends if you’ll get home from work after dark. Not much to be done about that.
But if you can ride during the day, you just have to be willing to bundle up, longe if they’re fresh, and be willing to be flexible. You may have a week you can’t ride due to weather and then two weeks you can. I shift from my normal “I need to ride 5-6 days a week” to “I will ride when the weather lets me.” That keeps me from being frustrated when I can’t ride. As others have mentioned, sometimes just doing walk and trot work can be beneficial.
Learn your footing and what preparation or maintenance will keep it as rideable as possible. Here in CO, the sun is warm enough that usually by mid day it’s thawed enough at least for a light ride, assuming we aren’t in a really cold snap.
I also always plan to give my mare at least a month or 6 weeks of a true vacation. One, I think it’s just good for them. Two, during the holidays or during when the weather is really crappy, it takes the pressure off. A little time off is good for everyone.