If you have the bicycle style ski helmet ( this is the high density styrofoam with a thin thermo-plastic shell over it ) do NOT paint it. The outer shell is ussually just taped on and the foam will definitely deteriorate either immediately or over time depending on the paint. Most helmets of this type are not taped at the vents and other openings so overspray is a given. Some helmets of this type have been molded to the foam by heat and pressure, this type helmet is baisically the same bike helmet construction, just a bit higher quality but the other worry with this type of helmet is the outer layer is not painted it is melt pigmented. If you apply a solvent base paint to this type plastic it will eventually dissolve the foam or weaken it at a minimum, due to a chemical property called plasticiser migration.
The other two types of helmets made for Skiing are ABS plastic (Brands live Uvex and POC use this). This is a MUCH better helmet.
Again they are colored through a process called melt pigmenting (more or less mixing the color into the plastic while liquid). There is a new paint on the market made just for plastic. If any paint is going to stick and not attack the ABS it would be this. I think Krylon is marketing it. While I doubt you will compromise the integrity by using a plasic type paint there are other pitfalls to painting out of a can. The biggest problem is they use more solvent in paint cans to thin the paint so it won't foul the nozzle. Because the paint is thin it tends to run if you get good coverage, if the coats are too light it will come out rough. You will also need to sand it with 800 grit sandpaper
then use "tack cloth" to clean it before painting. You will need a "clean room" , a cheap wayto do this is use newspaper to cover the walls or partition an area with newspaper, this will keep the dust out.
Don't use enamel (oil or acrylic) or nitro cellulose laquer, both are solvent based and will attack the ABS plastic. ABS plastic is the plastic used on ski sidewalls (except capped skis)
The last type of ski helmet is the older style UVEX. I am sure other companies made them. Back then helmets were used only in downhill. In 1977 they stopped requiring helmets for GS and with only racers wearing helmets then, there were few companies willing to make them. If you can find one of these it is fiberglass and strong.
They are lined like a motorcycle helmet and were lighter than a motorcycle helmet. These helmets you CAN paint with nitro cellulose laquer (these are the best paints in many respects , like candy apple, pearl, tinted clears,flip flop 2 color paint metal-flake etc.,but also the most difficult to apply), enamel, epoxy, anything you can paint a boat or car with. If you really want a custom helmet I would find a motorcycle shop and I am sure they can tell you who paints gas tanks and such.
If you just want to update your helmet I really think I would just get a new ABS helmet and see if you can find stickers. Painting any but the fiberglass helmets have too many safety concerns and the outcome is unpredictable at best. Or if you want to express yourself get an old UVEX helmet (they have a removeable face guard) and find a pro car painter to airbrush any design you want.
hope this helps