Light rain isn't too bad, but it's going to cut down on their efficiency and how much prey they can carry. If they get drenched, they won't be going much of anywhere until they dry and preen. Here's a wet/dry of the same owl:

Even the owls that primarily feed on fish don't submerge themselves and don't even like getting their feet wet for the most part.

Owl feathers don't have the feather barbs packed nearly as densely as most birds. If you hold an owl feather up to light next to another type of bird's feather, the owl feather is very transparent (and extra soft!) compared to say, a duck or hawk feathery. This lets air pass through, making flight quieter at the cost of efficiency (owls are pretty slow fliers and also mostly glide to hunt, making them even more silent), but those gaps really hinder their water resistance. The water will fill in those gaps meant for the air and get stuck in there. Flapping will shake some out, but if everything is just plain saturated, the barbs will all be too heavy with that water clinging on.

I need to just take a better pic myself to highlight the differences, but for now, here are some Short Eared Owl feathers and then a SEO flying in some fairly direct light. You can see the openness of the feathers letting the light through, and if it were raining, all that would be sponging up water.