Hike-a-bike on Speedplay is problematic as they get full of mud. Less of an issue on other cleat types
I've had SPDs so full of mud I couldn't clip in. It's more of a problem with some pedal designs than others and I don't know how they compare to Speedplays.
Normally when my SPDs clog up, I've managed to get them to engage with the pedal with a bit of violent stamping. Apart from one time with a clayish mud with plenty of fine gravel mixed in, well-compacted from wandering about a campsite. In the low temperature it had achieved the consistency of concrete, and was just sliding off the pedal. Had to dig it out with a twig.
I've got the ATACS muddy a few times on tilebagging adventures, without problems. They seem to behave about as well as SPDs, but perhaps slightly less inclined to clear the mud from around the cleat while pedalling, so it ends up on the carpet when you get home. They appear to be a popular cyclocross option, so they can't be too bad in muddy conditions.
I had the Looks fail to release once due to an innocent looking pebble caught in the mechanism, which would have been awkward if it had happened on the other foot. I've generally avoided exposing them to anything worse than a trackside puddle.