You may snowmobile to most 10th huts on trails that are perfectly legal for snowmobiling. When you arrive there is a non-motorized envelope that surrounds the hut: park outside the envelope and haul in your stuff.
Other posters are correct that this might be frowned upon. However, we have been using this method for about 10 years and have accessed many of the huts including Estin. We always reserve the entire hut, drive & park legally, and do our best to minimize impact on other trail users.
The main reason we do this is that we are able to bring all the beer, good food, etc. that we need for our group trip. We usually assign a few of us to snowmo duty (only need 2 sleds for a group of 16), the remainder carry their sleeping bags, safety gear, and other personal items. Be warned that the haul from legal snowmo parking to the hut can be tough-our snowmo team usually earns their keep. However, in the end the entire group is less fatigued meaning more energy to go skiing around the hut. We leave the snowmos parked until it is time to go home.
In regards to the ethical considerations, I find that 10th Mountain is a bit two-sided on this issue. They clearly discourage using snowmos in winter, but seem to have no problems with people using a 4x4 to access the huts as a support vehicle for summer biking trips. What is the difference? If anything a 4x4 will leave more impact...snowmos ride on snow that melts. We've also met 10th staff while at the huts on numerous occasions and they had no problems with our trip plan.
I've also heard the argument that one snowmo will bring more: this might be true, but that isn't a valid argument since the trails in question are all legal for snowmo use. Case in point at Estin: we were far from the first people to be snowmobiling in the vicinity of that hut! The rest of them were there to snowmo, not for the hut. Fortunately there is plenty of legal wilderness right behind the hut and we were able to find all the fresh we could eat
For those who would say that any snowmo use, legal or not, detracts from their back country experience: well, I agree that they can be annoying. The good news is that there are many, many places where you may find solitude since no snowmos are allowed! For Estin...just try the Ironedge trail. For trails where mixed use is legal, best to let everyone enjoy as they see fit and do your best to get along.