Sure, add on a third wheel, some thicker tires, and give me a cabin so I don't need to get too rained on and I can probably get rid of my car and borrow one if I need to pick up like a load of plywood or something.
Seriously though, a cabin probably won't even add too much weight, make it out of corrugated plastic or something. We already have the technology.
It varies from state to state but usually the deciding factor is the motor. No motor? It's a bike, no matter how many wheels it has.
Amusingly enough many of the laws are old enough that they are written with "cc" mentioned, below 60cc is a "moped" above is a "motorcycle". Those rules will have to be updated to account for various traction devices.
The balance requirement of a two-wheel vehicle probably makes them less appealing in icy weather to most folks. I don't live in an area that experiences cold weather, so I'm speculating.
They make electric trikes, and they're a bit more popular around here (Nova Scotia). Electric trikes have their own balance problems though. Also thinner tires and there being no such thing as ABS brakes make it really easy to go into a slide, especially if you don't really know why ABS brakes are a thing.
Cold weather is difficult, you need to protect yourself from the cold but you also need to deal with heat and sweat from biking, so your clothing requirements actually change depending on what point in the bike ride you're on.
Visibility is reduced due to high snowbanks, so you're likely coming to a complete stop more often than you otherwise would. That's a good argument for electrics and regenerative braking obviously.
Road salt and ice are a big problem, since bikes have components exposed. Components like chains, brake lines, the steering yolk, etc. Those are probably not made for the weather here and will more or less dissolve if you use most bikes during the winter. I'm sure there are some that are alright, but it's an additional research task.
I think it's solvable, and a personal vehicle that can solve that will probably do quite well if they can hit the right price-point, but I think that vehicle ends up looking more like a golf cart or a kei-car than a bike.
There's a subset of people who are very anti-car and not actually very pro-bike/transit and you can find them by seeing if they rant and rage against motorcycles as well.
Seriously though, a cabin probably won't even add too much weight, make it out of corrugated plastic or something. We already have the technology.
#legalize_tuk-tuks