Oyster spawn outdoors in winter?

I have an oyster mushroom spawn bag that is probably just about spent. How much winter can this spawn take, if I put it outdoors now? I'm in Anchorage, Alaska, so once winter hits, it can get very cold. Is the spawn likely to survive in the mulched gardens?

It will depend on the type of oyster mushroom.  Most of the bright coloured oysters (pink or yellow) are from tropical areas and for sure will not overwinter.  If the kit is pleurotus ostreatus oysters (majority of them are) there is a good chance it will over winter for you but depends on where the strain orginates from.  Pretty sure ostreatus is native to most areas from Alaska to Florida, so cold tolerance will differ greatly depending on the region it was acclimatized to.  Only one way to find out for sure!

It's the plain white oyster. The bag is from Fungi Perfecti, so it's probably a West Coast mushroom, but they are a lot warmer than here most of the time. However, my back yard garden beds are in a protected location and seldom suffer much from north or east winds because of the location of utility buildings and the house, which provide a lot of shelter.

I guess I have nothing to lose, so this weekend I'll crumble up the mass and put it iunder the mulching straw. I plan to sterilize some new straw and introduce a bit of the bag mycelium into a new bag also.

I am wondering about the cold also. ranch 1 is at 6800 ft in the Sierra Nevada range. We get about 10 ft snow pack but the summer should be fine would love to arrange a patch to see if it could winter.