Can you install tire chains on it?

I could probably install chains but wouldn't that just destroy the lawn and only give me traction every few inches in the rotation?

Look at tires with a more aggressive tread! Check with the tire sellers, to see in person, the types of treads that would serve you better.
Another thing to try would be only mow down hill, instead of both ways. Also, you could fashion a weight tray like some tractor owners put on their machines, to keep the front wheels on the ground when starting out up hill. Or, on the rear.
Another solution would be to install the engine from the Ariens into the old machine. Can you put the wheels from the old machine onto the Ariens? Might need a bit of figuring, since they are different.
Snapper warns buyers/ owners, to be careful when starting up-hill with a full bagger on the back! I find it a bit exhilarating when that happens. Sort of gives ya the feeling of riding a bucking bronco! I've never had mine tip over all the way. Yet---its a 1983 model.
The problem with tires not getting traction is why the tractor designers put those wide tires on the Craftsman lawn tractors! HTH: Rusty Jones

They put the smooth tires (and slick seat) on so that you don't overload the weak transmissions. :)

What you need are tires with ag treads (bars arranged in a broken V shape, like you see on large agricultural tractors). They offer much better grip - they are not offered as standard because they can tear up a lawn if you're not careful with them; however, as you have found out, you can actually do more damage with the smooth turf tires when they are not up to the job conditions.

If the ag tread tires (Carlisle makes 'em, do a web search) don't offer enough traction, put 5 gallons windshield washer fluid in each tire - that will give you an extra 70-80 lbs of weight right where you need it and actually lower your center of gravity (important on slopes). You can either put the fluid in by breaking one bead on your rim and pouring the fluid in, then resealing OR run it in through the valve stem (somebody posted on here not long ago about a method they use for going through the valve stem - involves using a garden pump sprayer inserted through the stem.

I've done both of those mods to my Craftsman DYS4500 LT and have no traction problems on the slopes in my hilly yard - I'm just waiting for the tranny to give out now... :) :(

A set of 2-link tire chains will give you enough traction and are less expensive than any pair of Ags would be. And if you find that you still have the odd bit of traction problems, then fill your rear tires with windshield washer antifreeze to 80 percent of the tire's volume. Inflate the tires to the normal pressure shown in you Operator's Manual. The tire loading will also make your tractor far more stable on those hills then you have had to date.

It will make your tractor feel quite different....in a positive way. I've given you a link below. The standard twisted link chains should be adequate but the V-Bar is also there for your consideration.

Here is a link that might be useful: chains

Yep a more Aggressive AG Style Tire will solve your slippage problems that you Turf Style Tread is causing as advised by Rusty GP and Komp. Eat a little more Steak and Potatoes , the Xtra Ballast won't hurt either lol .

I agree with adding washer fluid to the tires. Made a huge difference in mowing a difficult hillside. Lowers the center of gravity better than most other weight addition methods. I added washer fluid to the front tires as well to keep the wheels from pulling off the ground. I use a set of turf tires for mowing and a set of ag tires, also with washer fluid in them, for plowing snow. I even cut sipes into the bars on the ag tires to give me better grip on ice.

Also, lower the pressure in the rear tires. With or without washer fluid in the tires, a lower pressure will help the tire conform to the surface and reduce slippage. My rear tires are kept at about 6psi with the fluid filling about 80 percent of the tire. You'll have to judge how soft is still okay with your tractor tires, but in 6 years of use I've only popped a tire off the rim once due to low pressure.

Well I managed to find some Kenda Scorpion tires at a store near me for $45 each. http://www.blackforeststore.de/img/produkte/kenda_K290.jpg

I popped the old ones off the rims and put these on already. I haven't tried them yet because it just rained and it's really soggy now. From the sidewall, it appears these tires are designed to be run between 5-15psi so I'll probably run them at 5 and see what happens.

I definitely plan to run some water/antifreeze in the front tires for ballast to help prevent the nose from popping. I'll see how the rear tires do normally before putting fluid in them.

Just an update. The new tires work excellent! I got stuck once only because I was trying new mowing paths that I've never attempted before and it did all of them except one.

One word of caution to anyone considering different tires... If the tires start to spin you have to back off the throttle quickly or they will dig in hard.

I have a troybilt pony riding mower and I'm having the same trouble with it sliding down my hill. Was looking into a more aggressive tread tire but can't seem to find the size. Troybilt says it takes a 20x8-8 tire for the rear, but can't find that size in an aggressive tread. Any help plz.