If the OP has a 10k budget-he has a 10k budget. There is no way to get the best options for his property for that kind of money, and that's ok.
For 10k, I would be looking at either a used large garden tractor (like a JD 7xx), sold with a MMM and a plow or blower., or a used sub or compact tractor. I got $7500 in trade 10 years ago for a BX with 1200 hours, had MMM and FEL, and sold a
B2620 with FEL, 775 hours for 10k last year.
Both of those would have been great choices for the OP-would have had to add a RFM to the 2620, but $1500 will pick up a used one around here all day long. The other point to consider, is unlike old pick up plows and 50 year old tractors, equipment like I have mentioned is very reliable-certainly able to be used for at least several years with routine service and minor repairs. Now if the OP is mechanically handy, that old stuff may not be a problem-I'm not!
Obviously, a 35hp compact, a commercial ZTR, and a new 4wd truck with a plow would be the optimum solution for the OP. I have all these things except for the plow- but I didn't get them for 10k!!!!