If it was me, I would go for a small frame lightweight 30hp tractor. The Kubota B7800 (low price), B2910 (higher price, more features) or the new B3030 (soon to replace the B2910) all fit that bill very nicely. New Holland TC29 & TC33 are both fairly small 30/33hp tractors, but they are larger/heavier than the Kubotas I would select.
Now let me state why I would go with a small frame lightweight machine. Given the tasks you have outlined, I would also strongly prefer a HST machine over a gear machine.
#1, the smaller the machine the eaiser it will be to get in/out of the stalls.
#2, mucking the stalls is not heavy work, you don't need the biggest, baddest, meanest loader so a lighter weight machine will do the job without straining. This is going to be a regular task, every week, all year, buy a machine suited to this task.
#3, you will be mowing the lawn, low weight, small size & high (relative) PTO hp all fit perfectly into the equasion. Small size = greater manuverability = shorter mowing time! Low weight = less rutting of the yard. Higher PTO hp = mower deck. Mowing & bush hogging will be a large % of your tractoring hours, buy a machine suited to these tasks.
#4, keeping the 5 miles of road open during the winter is a big machine job unless the snow fall is 6" or less. I suspect that most of your snows would be modest snows, therefore you can get buy with a modest size/weight tractor. Realize that as a % of time spent doing jobs, snow removal will be very few hours relative to mowing.