How do you keep the inside of a tent clean when it's snowing?

Hopefully, you are wearing clothes in layers, which is the best way to trap enough air to insulate you effectively. Only the outer layer will be covered with snow. You can simply strip off the outer layer and leave it outside while the rest of you goes into the tent. Boots come off last, so that you can step out of them and into the dry space. If it is snowing so hard that you will get snow-covered again even in the minute or two it takes to take off the outer layer, then set up a "mud room" just outside the tent by laying one tarp on the ground and pitching the other as an awning. The inside of your tent is probably none too warm, especially when you first get into it, so don't fret if a bit of snow still gets in. Just sweep it out quickly with a whisk broom as if it were dust, before it has a chance to melt. (Of course, nothing that can't get wet should be too close to the door.)

take your shoes off just outside the door,or put a towel down on the inside of the door.

put a tarp down over your sleeping bags on which to change, and then remove it with the clothes inside. maybe?

First off, brush as much snow off your outer clothing as possible. Strip off that layer outside the tent. Sit down inside the tent with your feet outside (in the vestible if you have one). Remove boots without bringing them in the tent. Then brush them off and bring them inside. When camping in snowy conditions (rainy ones too, for that matter) I always include a sponge with my gear. While this wont eliminate water inside, it goes a long way towards minimizing the problem.

Take off your outside clothes and boot before you enter.

Take your clothes off outside. Hop into the tent really fast! That would work.

Beedsarefun is correct. I live in Alaska as well. If you have a 2 man tent in snow with no vestibule and do not have boots with removable inserts, your tent will be a mess. That is simply the truth. Also if you’re in the snow; you have to dry out your boots from the sweat you left in them, how can that be done with no removable insert in below freezing weather with out heat? Come on now people just think here please. The only other way to dry things out is to freeze dry them and this can take a few days and very cold temps are required. You need to buy a tent made for the snow instead of trying to get by with a summer tent. Winter tents have a vestibule they include them for this very reason. Or you can make one like the beedsare fellow suggested. I am trapping right now in Alaska and I am using a Cabela’s Outfitter tent with vestibule to park my snow machine in and shake off the snow. I also use a hand broom for this. When I left camp in the hands of my brother 2 days ago there was 4 feet of snow, since then we have gotten another 3 feet. When I get back with supplies I will be covered in powder snow and have no intention of bringing it in the main part of the tent. Our outfitter tent has a wood stove for heat and cooking. But as beedsare correctly said again, we never cook in the tent except when the bears hibernate otherwise you will have a very large uninvited guest! Snow will collapse the strongest tent, this is why my bro is there to rake the snow off with a snow rake, care must be taken not to tear the tent with the snow rake. I hope my answer helped you sir. I think we just have some here that are weekend campers who haven’t experienced living in the snow for months in a tent.

Keep dirty things in it's vestibule.........

good luck let me know when you fig-ger it out