Really not an issue. Siberia, like most of Central AK, is actually incredibly dry, and doesn't get much snow. What it gets, stays, but it isn't much. The icing will all be inside, not out, and the inside will melt off the snow that does land on it.
I actually live further north than both you and Mirnyy, in a very dry part of Scandinavia (Norway steals most of our snow), so I'm perhaps more experienced in what Siberian weather does/can do.
Mirnyy Weather
My current weather
Whilst snow flurries are intermittent they will block light, and once the temp starts descending to minus double figures it becomes a nightmare when it hits a relatively warm surface, melting, then refreezing into ice which then gets further insulated by additional snow landing atop it. Coming from Alaska I'm sure you've experienced this and know how much of a problem it is to scrape off. If I know snow is coming I generally turn off the heating inside my car for precisely this reason.
Even if it doesn't snow you still get constant ice crystal growths. Sometimes they are spiky formations which can get several centimetres thick (depending on ambient atmospheric moisture) and when it begins to get properly cold -10 down to -42 (which is the coldest we've had it here) you instead get very fine surface crystals which are translucent white but are a complete bugger to scrape off a glass surface.
This kind of crystal deposit/growth never stops because there's
always some degree of moisture in the atmosphere above you... especially when you are venting the transpired moisture of an entire city into the air above (or nearby) the dome. The walls of my house are currently covered in this particular whiteness, which in many places is reflective enough to hide the fact that the wall underneath is painted red. So you can guess how much solar energy that will cut.
Imagining that the warmth of the glass dome will simply melt such irritations is overlooking the fact that to enable a city like this to stay warm just using solar power, requires it be massively insulated. Its a catch 22. If you have the quadrupedal glazing necessary to let the light in but no heat out, it will become opaque from external frosting.
On the other hand, if you allow enough heat to escape through the dome to melt snow and ice, you're likely inputting far more energy than you are gaining from the light. Then you get the other problem you correctly pointed out, that of internal freezing, which is just as bad since scraping ice from the underside of a dome will be an even bigger problem and will still reduce light penetration. Believe me, when it drops to -20 outside you'd be struggling to keep the entire dome support structure from forming massive internal icicles - let alone melting off any external frosting.
You should see the condensation ice I have on the
inside of my triple glazing this morning, and it was only -19 last night and my house is heated to a nice toasty +20 with underfloor heating in every room.
