Having seen a bright pink one I would imagine the answer is yes!
No different to painting a car, metal bodywork will need primer, paint and topcoat if you are doing it proper like!
First thing to do is suss out what the panels are - if it's really really old, they'll be metal. If fairly old, they'll be wood. The newer type (mid 90's on) have coated panels which have an aluminium skin.
Haha I painted mine bright pink! Then blue, now red!! Did it with outdoor gloss from B & Q!! Not the best paint job in the world, but a guarantee that no one will pinch it!!
Its had a couple of panels replaced, and they are a different colour green and it looks quite odd! So I think maybe we (being the royal We!) has a job this weekend!!!
I bought an old red ifor that was turning pink! I used red car colour restores wax - one coat and it looked new - and the wax kept it for ages! ( about a year)!
But...what colour????? I dont want anything to much in your face, I quite like the black ones, we tow it with a green rangerover. So....do i go with the green, or the black??? Decisions decisions!!
I may be too late for you but....... The most important thing you'll need from B & Q is some emery paper or some kind of abrasive and some cellulose thinners - all the original painted panels would be done in spray paint which is most probably beyond your capablities but do give them all a light scratch and then a good clean - particular the joints and overlaps - then wiping everything with the thinners. Ordinary gloss paint will do as other posters have said but an undercoat too will make a better job - a brush finish is usually better than roller depending on your skill.
I have painted my ifor williams. I have one of the older ones that has wood panels and i used front door paint from B&Q. It only needed one coat and the paint i used had a built in sealer. I painted it a year ago and it still looks fab today after been un covered all year round.
Or you could get it wrapped, it will look more professionial and you can have any colour you like even mettalic! Go to www.motomode.com they have rejuevenated several old wagons to look better than new!
Use a small roller designed for yachts etc to get a good finish do not use cellulose thinners on gloss paint. Nowadays you can buy acrylic outdoor paints but this will not be what is required, you can use old fashioned gloss paint which needs white spirit thinners
Also consider spray cans. Most important is preparation and an undercoating is needed if changing from original to a gloss paint.
Use sugar soap to wash off all grease and dust residues.
Do not rush!