Rain has ZERO influence on the enemy, only on players. Enemies don't even wet from rain, otherwise they would take 50% more damage from Frostner. Which they don't.

Just seems odd that normally they are roving all over the dark forest (as it's right on the border), but when it rains I don't see a single one.

I'm still building there, so will take an opportunity next time it rains.

I'll run over and lure them back into the dark forest while raining.

It's a fair assumption, but...
The short answer is no, rain does not harm them.
No guesses, but we can examine the evidence if there is any ;)
I haven't seen it rain in the Ashlands.
The Surtling presence in the Swamps, where it can and does rain might be explained by the protection that the Fire Geysers provide.
Have you ever seen the Surtlings travel outside of the Ashlands other than a raid event?
When a "The smell is fading" event occurs, has it ever rained?
If and when that raid event occurs and it rains, then you'll have your proof one way or another...
Alternatively, you may accept the information the Wiki provides ;)

Originally posted by Wiki:

They are especially dangerous in groups, but are weak to Water and receive damage from it, although rain doesn't seem to bother them.

https://valheim.fandom.com/wiki/Surtling

Thanks.

And yes, as I am on the border of ashlands and dark forest, they are always coming over into the dark forest biome, which gets rain every so often.

While they always seem to cross over, during rain I don't see a single one.

it can be a storm outside and i get the event and it stops raining , the rain in the swamp is like a drizzle never seen them in the poring down rain

Normal and swamp rain dont really make "wet" on enemies , the wet debuff is that really kill surtlings
This can be tested with frostner or frozen arrows : most show u yellow numers ( weakness ) because make real wet on enemies ( makes them swim and next hit them ) do that , but rain didnt , them keep showing white numbers
Thats why surtling dont die for rain but them nearly blow up when touch a little body of water