One of the beauties of the Case tractor line is that the 200/400 series tractors share the exact same attachment mounting system.
Case made two SnoCasters (single stage) for their tractors. One is 48" wide and the other is 38" wide. The narrow one is meant for the 200 series and the wider one must be used on the 400 series or the tires will be driving on fresh snow and packing it down. The wider blower will work on the 224 and 226 models because they have enough hp to handle them. Your 12 hp 222 would best be served by the narrower model. A set of tire chains is highly desirable as is a weight box on the rear to offset the weight of the snocaster and put more weight on the rear wheels. Many users also fill the rear tires with windshield washer anti-freeze to increase traction.
Check on eBay using "case garden tractor" and "case lawn tractor" in the search box. Prices vary but you can expect to pay anywhere from fifty bucks for something really rough to five hundred for something in mint condition. Ingersoll bought the Case GT line in 1982 and by 1997, the tractors bore the Ingersoll name only.
Many of the Ingersoll branded blowers will work on your 222 but you need to be careful as to the year of manufacture. In the early part of the 2000's, Ingersoll turned the engines 180 degrees in the frame and this changed the direction of rotation for all belt driven implements.
As for your 222, if you don't have any service history on it, then one of the best things you can do for it is to flush the hydraulic system and install the correct oil. Remove the deck. Under the checkplate floor is the travel/lift valve. On the bottom of this valve is a hex head drain plug. Slip a drain pan under the tractor and open this plug.
Remove the spark plug and use the key to spin the engine over. This will pump the oil out of the reservoir. Put the plug back in and fill the reservoir with 20W50 motor oil such as Shell's Rotella T or equivalent. Put the spark plug back in, start the engine and use the tractor for ten to twenty hours and repeat the process.
All too often, people put the wrong oil in these tractors. They use hydraulic oil or auto transmission fluid and then wonder why the performance drops off. There is no filter on the system either and owners often neglect to change the fluid, thus allowing contaminants to circulate continuously and damage the pump and other components.