I have been lurking here for some time and have found the information very helpful...
I sort of came to the same decision point about 10 years ago when I bought my current property -- 5 acres, mix of grass/weeds (2 acres or so), and brush/trees (remaining 3). I knew I really wanted (needed) a compact tractor with FEL (and box scraper) for a variety of cleanup needs, but that it wouldn't do a nice job mowing the grass. Given the rough terrain in some areas, I also didn't think a ZT would work well, so I went with a large Craftsman "lawn tractor" -- T1600. I liked the riding mower because of the large deck, tight turning radius (18"), ability to mow in reverse (really handy), and it's powerful enough to pull various implements behind it when needed (
chipper or small trailer). I have to admit, I have abused the crap out of the mower and it's held up to the abuse. Aside from mowing the grass out front (can't really call it a lawn), I also use it for bush clearing (if I can get the front over it, the mower will chew it up) and hauling stuff around the yard. I have to replace the blades every season (due to chewing on brush and rocks), but I've yet to have to perform any maintenance other than regular oil changes and blowing out the air filter. I thought I'd kill the poor thing after a couple of years, but 9+ years in, it's still running great and keeps the grass looking nice in the spring. Picture to show some of the crap I mow with it.
On the tractor side, I couldn't afford a nice, new tractor and the riding mower, so I went with a 'grey market' Yanmar F18D with a generic box scraper and Koyker FEL -- picked it up for a bit over $5K at the time (2012) and it's been a workhorse ever since. My wife initially thought I just wanted a big toy, but after a few large jobs around the property (we had a lot of trees to clear), she told me it was one of the best purchases we ever made. I had to replace the diesel fuel return lines this year (pretty simple job) and that's been it. It's even running on the same battery it came with. Again, oil changes and blow out the filter and she's happy.
So, if you want the grass to look nice, go with a dedicated mower (I prefer the 'lawn tractor' over the ZT) and find a tractor that will suit your needs for the heavier stuff. There are a variety of choices out there now -- even newer options like Kioti, Mahindra, and even Yanmar coming back into the market, making the prices more competitive.
As for snow, I can't help you there. I'm in a SoCal semi-desert area, so we get a couple inches a year max.