@DogAndCat36 lets stop and regroup. It is a reasonable question and there could be some benefits. Or it could cause issues.
Your job is not to keep your chickens warm. Your job is to allow your chickens to keep themselves warm, just like the birds that overwinter there keep themselves warm without a lot of help from you. Wild birds can find protection from the wind. We need to build our coops so they are not exposed to a cold wind, even when on the roost sleeping.
At the same time they need to stay dry. Your biggest risk is not from them freezing to death but frostbite. If you walk outside in winter with wet skin you are at high risk from frostbite. If that skin is dry you are at a much lower risk. Moist air puts you at higher risk than dry air.
In a coop moisture can come from their breathe, from fresh unfrozen poop, or maybe from a waterer. Good ventilation allows that moisture to escape. To me the best way to provide that ventilation and keep them out of a wind is to have the ventilation up high o any breezes flows over their heads, including when they are on the roost.
I'll include a link to an article by someone who lives in colder winter than you will probably see. You might find it helpful.
Alaskan’s Article
https://www.backyardchickens.com/articles/cold-weather-poultry-housing-and-care.72010/
Packing snow around your coop will provide insulation. That's just physics. As long as you don't block ventilation or doorways or restrict access to the coop for you or a way for them to get out of the coop if they want to go outside it will not hurt. How much will it help? Some but not a lot. In cold snaps it will cool off a little slower. With decent ventilation it will still get really cold in there but it may keep an egg from freezing quite as fast if yours lay this winter. If your playhouse coop is in the ground the ground underneath will act like a thermal mass in your cold snaps, a little extra insulation may get a little more benefit from that.
To me insulating it with snow while watching out for ventilation and access will not have life-altering benefits but you might notice a difference. I don't see where it will hurt as long as you take basic precautions.
