It all depends on what sort of 22 rimfire we are talking about, and what discipline we are shooting.
If it is a super-accurate bench rest unit, you will be cleaning more frequently.
Generally, if you want to shoot high scores, cleaning will be done every 2-300 rounds or sometimes less.
If we are talking your "plinker" or "grouse-getter" the cleaning interval may be quite long.
I have seen many 22's that have not seen a decent cleaning for thousands of rounds.
Semi-auto rifles need more frequent attention simply because the blowback action types used contaminate the bolt and action area.
One thing that many rimfire shooters are not aware of is the "ring" that is deposited just ahead of the case mouth in the chamber/leade area.
This ring is composed of lead and carbon, and has a marginal effect on standard chambers, but is deadly to match chamber accuracy, and must be removed quite often.
Some BR shooters clean it out after every 50 shot string.
In cleaning a rimfire, one must be careful to not damage the rifling since 22 rimfire barrels tend to be fairly soft.
Boresnakes are not great to clean any rifle with unless you wash them between each use. [You just drag dirt and grit back through the bore unless they are clean]
Boreguides and properly sized, one-piece rods are essential. [I prefer a coated rod, myself]
Aluminum is a poor metal for cleaning rods since aluminum oxides that form on the rod occasionally are very hard, and will scratch the bore easily.
As a last thought, I would never clean a 22 from the muzzle if it was humanly possible to clean it from the breech.
Regards, Eagleye.