This is a follow up to my question purely about lawn mowers.
We are short of space so having a lawn mower in addition to a snowblower is going to be a chore.
Is there a two-in-one device that has both attachments?
You say "snowblower" but you talk about "pushing" snow. These are two fundamentally different operations. A snowblower sucks up snow and ejects it from a chute so that it lands many feet away from the machine. A snow plow pushes snow, basically scraping it from the ground and pushing it somewhere else.
I'll address both.
(Disclaimer: I haven't used a snowblower or plow on a subcompact ("lawn") tractor. I have used both attachments on compact tractors (20-30 HP diesel tractors, with hydraulics and 4wd, weighing 2000-3000 lb.) I currently use a plow on a 30 HP machine. We get 48+" of snowfall annually, any time from October to April. I maintain a partly paved, partly gravel driveway about 250' long.)
You will want a machine that can handle driving around in the snow. All else equal, I'd want a heavy machine with good tire tread. If you're willing to mess with chains, make sure the drive tires will accept it. Four wheel drive could be a consideration.
You want a machine that has good lighting. Winter is dark. You'll be removing snow in the dark, in a snowstorm. It's good to not only see where you are going, but for cars to be able to see you when you're working at the end of your driveway.
First consideration: make sure your tractor will accept a snowblower attachment! If possible, I would buy both the tractor and the attachment from the same vendor, to ensure that they will mate.
If you get a lot of heavy snow, definitely consider a two stage snowblower attachment. This will eject the snow with more force, sending it further.
If you have a stone/gravel driveway, you should seriously reconsider the idea of snowblowing. When the snowblower digs in below the snow, it acts like a machine gun, sending rocks flying. You will need to add skids to the bottom of the snowblower deck to avoid this dangerous situation. (I've done it, but I never liked it and I no longer do it this way.)
You are going to blow snow in windy conditions. This sucks: you get tons of snow blown back in your face. So if the tractor accepts a cab or "windshield", this is something to keep in mind.
Obligatory safety notes: Never aim the snowblower at the road. Sending a stone or hunk of ice at a car would be bad. Never aim the snowblower at the house; a hunk of ice through your kitchen window when it's 20F, snowing, and windy will ruin your day. Never aim the snowblower at people or pets. I mention this now so that you can plan how you're going to use the snowblower and where you're going to (safely) put the snow.
Again, make sure your tractor will accept a snowblower attachment; buy from the same vendor if possible.
Weight and traction are critical if you're going to push snow. (My tractor weighs 3000+ pounds, has industrial-tread tires, 4wd, and still spins when the driveway is slippery...)
Another consideration is where you're going to push the snow. If you get a lot of snow, you'll have to push the first snowfalls well out of the way so that you have room to push later snowfalls. This implies that the control mechanism on your blade is important; most consumer grade lawn tractor attachments I've seen are simple hand-operated levers to raise/lower the blade. This means you can only push snow forward, you can't lift it at all. If you can't push the snow up, you have to push it further to make room for later snowfall. If you have to push it onto your lawn, you risk digging up the lawn, either with the blade or when your wheels spin. (I have the benefit of hydraulics on my blade, so I can raise the blade when I push and make high snowbanks. It makes a big difference.)