Geese are wonderful but they can take some managing. I don't know how to tell with Romans which is the male or female other than turning them upside down and checking it out. Even then, if you're not accustomed to sexing geese it is possible to make mistakes, particularly with young ones. With most geese there are clues. The females have deep voices and make conversational noises. The males are shrill and tend to call. The males also have a more vertical stance and hold their heads high. The females are more demure.

Two nice things about Pilgrims (I have a trio) is that they are seldom aggressive and it is easy to tell at a glance which are males and which are females. They are really sweet geese, but some of them are easily bullied by more aggressive species. If you are going to add Pilgrims, if you can get the Romans to adopt them as babies there is a better chance of them all getting along.

Are you planning to breed your geese? If so, you need to realize that to have purebreds you must keep the breeds totally separate during the breeding season. (Approximately February to June.) Otherwise you will have crossbreeds, which are harder to sell and bring very little. If you are raising geese solely for your own table, this is less of an issue, but still should be kept in mind.

A ten by ten building is certainly big enough for four geese and I have always locked mine in at night. You should put hardware cloth over those windows from the inside because predators can tear through screens like it is paper.

Sounds like you give your geese plenty of care in the bedding department. My geese only make a "nest" when they are laying eggs. Otherwise they just plop down where they please, usually near the water bucket. If you feed the geese in their house then they need water as well.

Don't worry about leaving the half-door open in winter - it's okay. Just make sure there is a hook so it doesn't slam shut and block them out. Geese are extremely hardy and usually prefer to be outdoors, but they need to have the choice to get out of the weather. Most of the time when their feet get cold they lay down on the snow and pull their feet up into their downy feathers to warm them. They will shove their bill deep into their back feathers to warm it as well. The rest of the goose is weatherproof. :)

I think the ventilation from the open door keeps the odours down and makes them healthier. My geese have their "pop-hole" on the south side, which helps, since the wind is usually westerly or northerly. The breeds with knobs on their bills can suffer from frostbite there, but the ones descended from the European greylag (includes Pilgrims and Romans, Toulouse, American Buffs, Embdems etc.)

We are in Zone 5 and can also get some very cold weather. There were two days last winter when I kept the geese inside... The snow was too deep to graze and the cold and wind were bitter. They weren't happy about it but it didn't hurt them to stay in. Some other cold days, I only let them out for the mid-day hours... about 11 am. to 3 pm. Since I feed them when I put them in for the night, they are usually amenable. In any case, they are easily herded unless they are in a naughty mood and want to play catch-me-if-you-can.

My geese prefer their feed (organic chicken mash and/or scratch) wet and I am glad of this. If they leave some in winter, there is no danger of them eating dry food after the water bucket freezes. The feed freezes first. Geese can be susceptible to choking if they are eating grain etc. with no water available. A heated bucket is a good idea.

I hope you can sort through this hodge-podge and pull the information that is of use to you. I'm afraid I just blurted. But I think it addresses most of your concerns.