To address a few issues people have brought up:
There's no "our side" of the driveway. The way it's set up, everyone uses the whole thing, and it makes no sense to clear half of it.
I already have to get up at 6:30 to get to work, so it's not a question of "sleep in and clear the driveway at 9:30", which I also wouldn't have a problem with, and am happy to do an weekends. I'd have to get up even earlier to make time for shovelling, and it's already killing me to get up at the time I do.
My boyfriend and his sister jointly own the house, so there's no issue with any leases. The driveway is already heavily ice-damaged and rutted, so while it can certainly get worse, it's not a question of preserving a nice flawless surface.
There's no legal liability. This isn't the place to get into a discussion of local laws, so please take my word for it.
So far, it's only ever snowed overnight for some reason. I'll certainly take over shovelling if it does ever snow in the afternoon, but it would not be an equal division of labor at all, and I don't think Tom would be satisfied with it - his problem is he hates shovelling snow at 6:30 as much as I do, and doesn't want to do it either, but unlike me he believes it has to be done, and so he wants us to do half of it.
I'm aware snow is a lot harder to clear once it's been driven over and melted and refrozen, but I'd rather work three times as hard at 19:00 than get up a minute earlier than I have to in the morning.
My boyfriend refuses to do any shovelling whatsoever. If it gets above a foot and becomes an actual inconvenience to the cars, he'll pay for the neighbor to come with the snow plow. This was a point of contention before I ever moved here, but unlike me my boyfriend doesn't care if people get pissed at him.
There's also a summer version of this argument, where my boyfriend and me think that a garden needs to be mowed about twice a summer or so and looks fine as a wildflowery meadow, while SIL and Tom keep a fussy flower bed and a vegetable garden they want our help with. (I have zero guilty conscience towards our neighbors for our slightly messy garden. One has as giant junk heap of might-be-useful-at-some-point car parts, and the other one, a farmer, has a literal dungheap right up against our fence that stinks up the place in the summer.)
I'm aware that I could give in and do the shovelling and mowing on occasion to keep the neighborly peace, but, well. Half the reason I moved here was to get away from my mom and her insistence on me doing chores I considered unneccessary, but did anyway to keep the peace. So I guess I'm not in an entirely rational mood about this kind of request right now.
I'm certainly happy to do other small neighborly favors for them, like pen their chickens, or be available if their kids need someone while the parents are out at night. We'll also cook for each other sometimes. This isn't a giant friendship-ending argument, but it does create tensions.