Radica, were these growing in grass? I think this is actually Panaeolina foenisecii.
Frog has got it- It is Sarcosphaera coronaria. http://www.mushroomexpert.com/sarcosphaera_coronaria.html
I see Stropharia ambigua in the Fall, Winter, and Spring in Northern California.
If you can get better photos and we can be more certain of what this is. Though I am 97% sure this is a Conocybe species. Maybe C. tenera,...
Looks like a Conocybe. http://www.mushroomobserver.org/observer/advanced_obj_search?search[name]=conocybe+sp.&search[type]=Observation
Precisely, it is really a matter of priorities. I do not like struggling with people on the point of actually picking the mushroom if they are...
Oh jeez, there are so many that look like that... To narrow it down to species we would need more photos, and to know what trees and bushes were...
Wow, really? That is ice?? That is crazy..
California has dry weather... I find lots of different species in many genera that get this cracked pileus... Agrocybe, Leratiomyces,...
It is Inocybe, as mycomania said. It is definitely not a Psathyrella nor Galerina.
Those poor Armillaria have had a rough life. Armillaria, "Honey Mushrooms" can be quite variable in appearance!