Trying to blow snow with a ride on lawn mower is a bad idea. Blowing snow with a 1500 pound garden tractor is doable, with weight and chains added.
Less expensive riding lawn mowers just don't have the frame strength, or the transmission, to hold up to non mowing activities, regardless of what the fancy
brochure says. And if you have hills, which you do, this forum is littered with posts of guys getting half way up the hill and the unit just stops.
You also have to avoid pulling any heavy loads with a lawn tractor. Some inexpensive garden tractors look a lot stronger than they are. They are made to get you to
buy them, not to hold up a long time...
My suggestion for keeping costs down is to get a 3 series or equivalent JD riding mower for your lawn and those slopes, and then get a separate snow blower.
To get a machine capable of blowing snow and lasting more than a year or two will cost you in the 5-10K range used.
Reliability plus ride on plus snow is not cheap. So many good used SCUTS could work nicely for you. I'd keep my eye on a used BX Kubota.
Btw, I own JD, Gravely and CC garden tractors, all for different applications. The frame on the CC flexes when I drive it on my trailer. You do not want to overburden
these inexpensive machines or something is going to break sooner vs later.
I hear the message here don't try to make a lawn mower do what a small tractor was designed for.
Alternatively, no small tractor will mow grass anywhere near as efficiently as a regular mower, any kind of mower, but you have a very small lawn
so who cares. You want a Swiss Army Knife, look at the smallest Kubotas. You can find them used under 10K with low hours and MMM.
Just make sure the slope of those hills are safe, the bigger the unit you drive on them, usually the higher the center of gravity.
Kawasaki gas engines are usually the safest choice for longevity, but a Briggs Vanguard is a nice engine too. If you buy used, determining how well basic maintenance was done, like oil changes and filters, is going to be important. This is where buying from someone you know, or can trust, is a big plus.