Unless you are guaranteed that the hay or straw (doesn't matter, they both are notorious for seeds) are cleaned for seeds don't use them. You can't imagine the mess in the spring (believe me, I know). What you can use are leaves, ground or not, but ground is better. You can do this with a chipper/shredder if you have one, or a lawn mower and crunch them up. Pine needles will also work famously if you have any. I'm always in favor of leaf mold. It's full of nutrients and is the fastest and best way to enrich the soil. Mulch is good too, but it's expensive.

probably so ... if they are zone appropriate... then let ma nature take care of them... the media in the pot is key .... along with drainage ... and no sun on the pots .... the key: GET THEM DORMANT .. KEEP THEM DORMANT ... once you start caring too much.. loving them too much... in my experience.. you simply end up screwing up one of the variables .. in my high drainage native sand.. i can simply heal in.. pot and all .... ken

In addition to that, a refrigerator will desiccate them, even inside a typical plastic bag. We think of plastic bags as being completely impervious to water, but they aren't. If you place a damp paper towel in a ziplock bag, stick it in the refrigerator, and come back three months later, you'll have a completely dry paper towel probably covered in dormant mold (mold spores go dormant once they dry out). Some plants will also go into a deeper dormant state when stored in refrigerated conditions. In some cases, a process called sweating may be required to get them to come out of dormancy. It is possible to store trees in a refrigerator, but why would you want to with all the potential problems? You don't say where you are, but then, if you were living in an area that doesn't have sufficient cold weather to satisfy dormancy periods, why would you be growing them?

Dormancy starts setting in below 45F but above 32F. This when all the biological changes are happening to prepare for winter. Plants have to spent certain number of hours between these two temperatures to get them fully ready. Usuallit is about 1000 hrs. After that the plant is just sleeping. Maple roots are good to about 20F so they need a lot of protection. Conifers can go below but still should be protected well. Unheated garage works well but may need more insulation if it gets way too cold for extended period. I have an unheated "greenhouse" sort of. Made with EMT tubes and covered in white plastic that cuts down the light by 70%. The white plastic reduces the temperature swings during winter since it cuts of most of the Sunlight. Inside I bury the pots in soil and cover with leaf mulch. Conifers also stay inside that structure but lightly covered in leaf mulch. I shovel in snow when I can - it provides water and is also a good insulator. Some plants are overwintered in my unheated detached shed. Unheated basement can still be too warm. It needs to be below 45F. Deciduous do not need light but conifers do. They can still photosynthesize above 32F although at a very low level.