i have a 1997 345 along with the 42 snow thrower, and the 48 mowing deck with the power bagger (great for fall leaf cleanup). It's a great machine. I bought it used about 17 years ago, no major issues. I have about 500 hours on it now using it for mowing around the house and clearing snow.
It works great for snow removal up to about 7 or 8 inches of powdery snow. If the snow is wet, then don't let it get deeper than 4 or 5 inches otherwise you'll start to smell the rubber belt on the snow thrower slipping. If it's a heavy snow storm, I just go out several times to clear the snow away. It's fun clearing snow with the tractor, so I don't mind. No issues with the thrower clogging either, as the power of the tractor pushing into the snow just forces any clog out.
It is somewhat traction limited though on steep hills or if the rear wheels get into a few inches of snow. My 345 came with tire chains and rear weights, which are absolutely required. My driveway is pretty steep downhill towards the street. I can always snow throw downhill, and can usually clear snow back up the hill unless the snow is really wet and heavy. I can always drive back up hill on the cleared part of the driveway and then snow throw coming back down. The other trick is to slightly lift up the snow thrower to reduce the weight dragging on the ground, especially if your having trouble steering in the snow. The lack of 4 wheel drive or a locking rear differential is really only a problem if trying to deal with really deep (foot plus), heavy snow or with steep hills when there is a coating of ice under the snow.
Once you get the hang of it, it does a really amazing job moving snow.
The snow thrower belt is really the weak part of the system as it will wear out and it's about $50 for a new one. I'm on my 3rd one. The snow thrower will also require shoe replacement and scraper blade replacement depending on how much it's used.
This past year, the seals on the engine valve covers started to leak. I picked up new gaskets from the dealer, easy to replace, and it's been fine since. This had to be fixed since the leaking oil was dripping onto the exhaust.
My tractor has the plastic cam gear. I had a discussion with my dealer about replacing it and we came to the conclusion to just leave it in place instead of spending a lot of money on parts and labor to fix. They said they had seen 345 tractors with over a 1000 hours on them without the cam gear breaking.