While "Welcome to my house" is the only one of pair we would say upon greeting a visitor, away from the building and at a different time from a visit, one could also invite a visitor by saying, "You are welcome to my house." I find "welcome in my house" unnatural as an invitation; perhaps it is the usual usage in other forms of English, or a personal peculiarity.
I was interested in the replies from other members to your question, Ticcota. If you told me "You're welcome in my house", I'd think that you were taking special pains to be courteous. I agree with Parla's observation that using "You're welcome in my house" would work well whether we were in your house or not. Saying "Welcome to my house" sounds more like a standard greeting to a visitor who has arrived at your house.
Welcome to my house <-- used as a sort of greeting when someone arrives at your house
You are welcome in my house <-- a general invitation, but a bit odd You are welcome at my house <-- better You are welcome to my house <-- odd, in my opinion
I think the invitation sentence would be better with an any time, as follows:
You are welcome any time at my house.
It's also very common to specify exactly what they are welcome to do. For example:
You're welcome to stay at my house.
You're welcome to crash at my house.
You're welcome to eat dinner at my house.
You're welcome to come study at my house.
So I think the reason why the general You are welcome at my house is better with at than with to is that these longer forms usually have at. (The only exception I can think of is You are welcome to come to my house.)
I find "You're welcome in my house," somewhat odd, a touch eccentric, quaint, unusual ... ... but I know what it means.
"You're welcome to my house," could be more confusing.
I don't know if this OED sense prevails in all English-speaking regions, but it is very real here: e. you are welcome (to something): said ironically of something one is glad to be without.