You don't say how steep your slopes are. Mine range up to 22 degrees. Traction will be the major issue here and I found that only a locking differential gave me enough traction to mow that steep a slope. The first tractor I had, even though it was supposedly a "garden tractor", did not have a locking differential and would slip a wheel on the steepest parts of the slope, especially if the grass was just a little bit wet, which it almost always is here in western Washington. I decided I needed something better after it slipped sideways once and nearly tipped over. I sold that tractor and got one with a locking differential and haven't had a problem since.

My slope is 20 degrees +, my old mower was a mtd. I had to use chains to go up the slope if it was wet. A bigger problem was going down & turning. It would gain speed going down, over revving the engine and going much faster then the machine was designed for (my wife is glad to see me replace it). It was also very unstable when turning on the slope. I'm looking at a JD LA165, Cub Cadet LTX1046VT and Craftman Pro, but none of them list a "locking differential".

you are not going to find any tractor rated for that slope in teh sub 2000.00 range unless you look at older used GARDEN tractors. and even so you do not turn when going down that steep.

do you own a ATV? if so look into a Swisher mower to tow behind it. much safer than a LT.

The closest NEW tractor-mower with locking diff you'll find for that price is the Husqvarna 2346XLS, apparently around $2500.00. Plus, it has a 23HP B&S Vanguard (premium) engine. Check the link below.

Bill

Here is a link that might be useful: Husqvarna 2346XLS

Here we go again. Why wouldn't you buy the best you can afford? Unless you are moving in the next couple of years.
One good machine commerical quality will out last 3-4 of the light weight, lightly made big box models. I have a commercial ZTR, that would handle your slope with no problem, it would go places a yard tractor would not even try. On a slope like you have (I have had at least that steep if not worse.) I can traverse, go up and down backward and forward and spin around in place and go back the same direction all without the least fear of flipping or uneasy ness.

Just for kidks and giggles read this short biased I admit treatise on mowers and slopes. Scroll down a short ways down the page to see the text on hills and slopes.

Here is a link that might be useful: Click here

Looks like I'll be checking out the 2346XLS this weekend.

I have the craftsman professional 24 hp, 42 inch deck. I have a steep yard and wanted the stronger engine for climbing and engine braking. I bought it on close out at the end of last fall for $1400. It came stock with carlisle turf tires which spin like mad and tear up my yard on the incline. I ordered a pair of carlisle super lugs and rims, complete for about $200. Clearance is tight with the superlugs, but only a hair tighter than with the turf tires. On the carlisle page, you will see that the super lugs are only 1/2 inch bigger in diameter than the turf tires, and only have an impact of 1/4 inch on deck clearance. Superlugs installed, the professional climbs inclines like a goat, no weight added. I would agree on the turning part, my preferred method is to back down the hill rather than turn on the pitch.

I definitely agree with billbennett. I have Carlisle Tru Power tires (almost identical to super lug but with more ribs) on my tractor. I went a step further and filled them with 12 gallons of windshield washer fluid. The tires cost about $200 (for big 23" tires) with shipping on eBay. The mower has absolutely no problem climbing up out of the drainage ditch in my front yard, which is deep enough for my 4-year-old to disappear from view when he walks in it. I'd bet my open-differential filled-ag-tire tractor has superior traction to a locking-differential turf-tire tractor.
So long story short, you won't find a locking-diff tractor in the sub-$2k range, but you will find a good $1400 Craftsman that will suit your needs just find, and for another $150 (they get a lot cheaper as you go smaller), you can add ag tires, fill them with fluid, and end up with better traction and a lower center of gravity.
See the "traction" thread for pics.

I am going to answer from a different angle. The only thing worse than one slipping wheel is two slipping wheels. This spells trouble. I doubt your entire property is on a a huge angle. Why don't you get a push mower for the hilly parts, and a riding one for the flatter spots. A 300lb tractor falling on you is bad. A 800lb tractor falling on you may kill you. Is that the path you really want to take. Hills and tractors don't really go well together. Not to mention mowing straight up a steep hill over long periods of time will kill your transmission.

to follow on zoulas' comment: replant the sharp hillsides to no/low maintenance cover... and live to enjoy yer gkids. Playing humpty Dumpty with a running tractor ain't too swift IMHO.

Well of course you shouldn't do anything stupid like turn on a steep slope where you have the chance of tumbling down the hill. Planting dwarf junipers or thyme or something on a steep slope is definitely a better alternative to mowing. But some people have a bona-fide need to mow with a tractor on slopes.
I'm just saying if it's traction you seek, there are other alternatives to a locking differential. Concerning stability and grip, there are three things you need to consider with regard to configuration (coming from someone who grew up in the Poconos, mowing two mountainside acres with my grandfather's open-differential Gravely 8123):
1) Get a garden tractor with reversible wheels, and mount them on the wide (concave) setting.
2) Get high traction tires, such as HDAP, AG, or use chains year-round.
3) Add ballast down low, either by filling the tires, bolting on cast iron weights, or both.

I have a Kubota B-2400 4x4 diesel tractor with a 60" deck and a 20 degree slope/ No issues going up or down, ( as long as ther is a flat spot on top to turn around).
But now that is gone and I too need somthing that can turn on the slope. I guess it must be a walk-behind. but what kind will "walk up and crawl down with out tearing up the turf?