The thing about rain is it can look worse from a distance than when you're actually in it. It's a bit like driving in rain...if the vis is such that you can't see,say, twice your easy turn radius, you should be turning around. keep an eye on the weather behind you, constantly monitor the visibility, configure the aeroplane accordingly, always have a good plan b, in short, use what you were taught in the bad wx low flying part of the training. (And yes, carb heat, and windscreen demist.)
'Tis better to grow accustomed to what this sort of thing is like in light rain first (or not too low a cloud base, or not too much turbulence), in an area you know, in a controlled circumstance, before you find yourself in it up to the neck.
Next time the weather is a bit manky, go and do a local, with an instructor if you lack confidence, get a feel for it.
It's actually not too bad unless you're caught out with no experience.