you can paint them with craft or latex paint and then use a water based varathane over the paint..satin, so it's not shiny, but they'll be protected.
the question is, do you like/ love them? is there something you'd rather have? can you find someone to give them to? can you re purpose them in some way?
for other outdoor items, there are different sorts of paint. there's a new spray paint for plastic, there are special paints for metal....check home depot. places like that are very good about providing advice:)

If they're plaster or ceramic, you can use acrylic paint. Spray or brush on a polyurethane that is designated for Exterior... I paint all the time.. I just finished painting a satalite dish for someone. It was a contract job..

But I've painted ceramics, plaster, metal and numerous other surfaces that were to be displayed out doors. The paint you use really doesn't make that much difference except on the surface you are applying it to.. (if the surface is pourous, you might want to coat it first with a sealer so it doesn't absorb your paint)

The main thing about outside projects is that they need several coats of sealer. For the gnomes, I would recommend 3 coats of spray or 2 coats of brush on polyurethane or sealant. (make sure to seal the bottom as well.. and let each coat dry really well before applying the next one.)