Hard to ID from that. It's nothing to worry about though. Yes, the weather has a lot of affect on mushrooms- in wet years you get many more because they need moisture to send up the mushrooms. They are probably growing in your mulch- many of the mushroom mycelium (the part that grows underground- sort of the roots) are wood rotting types. I get the same kind you've pictured here on mulch in wet and in dryer years when it rains. It has never seemed to hurt anything. If you're concerned with pets ingesting some you can always pick the shrooms so they cant eat them, but most animals are fairly savvy about not eating poisonous stuff.