It’s mostly two bolts on an Ariens and the tractor can be separated from the intake housing. There are sum supplementary things depending on the model like the chute worm or chute connection to the head – minor stuff to disconnect.
You did not give your model but guessing it’s an ST824 924050 type. Sticking through the bucket is the auger drive shaft arm, through it’s support bearing, to a big pulley in the tractor area near the back of the intake housing. Remove the bolts and belt and the housing is separated.
The drive comes from a dual belted drive pulley on the crankshaft. The forward on drives the big auger drive pulley and the back one drives the tractor wheels.
For an older model 10000 series they had big knuckles to mate the tractor section to the intake housing for drive instead of a big pulley at the back of the intake housing. I’m not sure how far past the 70’s the 10000 series went.
Painting would be a good summer job. There are great rust dissolvers and inhibitors these days like “Must of Rust”. Harbor Freight has a decent inhibitor. I buy it by the gallon and spray machines constantly working down rust. Depending on the condition of the rust, it leaves the gray metal finish or black coat. You can brush off the white powder it leaves and paint over it. Rustoleum Safety Orange is a decent match for most years of Ariens but you can take a good size chip and have them match it with Rustoleum. Rustoleum primer is good to use. After a day of snowblowing and brushing off the snow and letting the machine dry off with the thin layer of dirt that always happens the paint will look original. You can go for a car finish but it’s a snowblower.
For what else can you do. Summer would be a good time to put it up on it’s bucket and juice the impeller pulley to shaft area with PB Blaster. Let it sink in for several hours. Someday you might want to replace parts in there and hub the pulley is connected to is a bear to get off because it’s a damp area and always rusted on. It would be a good time to coat the inside of the bucket. A few layers on the inside of the chute. I’m looking for some tough car finish clear to try on the inside of the chute.