It has been a great winter for slugs and snails, but why do they and woodlice, climb up the wall beside my back door. There is nothing to eat on a cream coloured painted wall! The wall may be warm, but even so, their climb seems pointless!

I guess you're just lucky...

This came up on Google:
"One theory is that when they want to rest, climbing up a vertical surface gets them away from predators, like rodents and some beetles that might attack them on the ground. If birds come for them, they may well dislodge the snail without getting hold of it, and it drops into vegetation below and evades capture."
Makes sense to me.

I've only seen snails do that. I think it's because they're just dumb. They get an inner urge to travel, seek new chomping grounds, etc. due to some environmental clue, and meet a vertical surface, but don't know if it's just a little obstacle or a wall that goes up and up and up.

Snails will even climb trees. I've found many big garden snails 10 or 12 feet up on tree branches.

Snails climb concrete walls because of the limestone in cement. It is part of their nutrient demand.
Also snails and slugs used to climb the glass walls of my greenhouse all the time. You could see "their feeding trails" etched on the glass walls. Those trails were left by their mouth parts as they fed on algae, fungus and other biotics growing on the glass.
It comes down to a food source.

Sometimes solving a problem is like a marriage. You find out what works and don't question why. When I see slugs climbing up my wall I just grab them and throw them in a bucket to get rid of them. I also think it is senseless for them to climb up a blank wall but I'm not going to try to figure it out. Grab them and throw them away.

If you grab them to throw them away be sure you wear gloves!

Snails and slugs can be infested with rat lungworm and larvae can be present on their surface mucous. It's rare in most of the continental USA but why take a chance?

Pat