Yes - though it won't be very pleasant, you get soaked, and I wouldn't recommend using an electric hedge trimmer in those conditions, too dangerous, but a pair of shears will be fine.

Yes, but don't use an electric trimmer - it could get exciting!

Even with hand trimmers, they will be more likely to mash the twigs, rather than cut them cleanly. Trampling the wet soil around the base of the hedge is not a good thing, either, especially if there is any clay in the soil.