I think you did great.
When anyone has nightmares, the first help is to assure her (or him, does not matter) that there is a safe place for her.
Just holding her and say that everything is ok now, that you are here to protect her from anything - it is the first thing and most important, of what you can do. (At my personal experience it is more important than saying that no danger exists - as for her the mummies and skeletons are really real, sometimes even more, than what she can see or touch. I remember nightmares, that continued, while I was awake and I did really see them. So be it, maybe they are real, but she is safe now. THAT is important in the first moment.)
I personally would not try to deny her nightmare or try to make fun of it, while she is still under its influence. But maybe some next day (if she remembers the nightmare, but it is "long ago" gone,) you may talk to her more about mummies and in the light of the day make speculations about how would mummy use toilet paper or something like that ... or talk to her more about how the mummy was really done and that all those wraps are glued tightly together, so the mummy could not move, if it was done right. And fake mummy is not a real mummy, but maybe somebody in costume. Or maybe not talk about it at all, if she did not bring it up, you know her better, than any of us.
The next thing, when the nightmare is not so intensive or when ended is to provide some help and point the thinking in another direction. Your explanation about open windows is a nice rationalisation, why she had that dream and she accepted it, so it worked nicely. (It may or may not be the true reason, probably there was at least something else, then just cold, but if she believes, that it had just this simple reason and that the reason was removed, then she thinks the right way and she knows, that no more skeletons will come this night. And so no more skeletons will come.)
You did really, really well, that you listened to her seriously. For her that nightmare was real and you did trust her and so you could help her. It does not matter, how realistic it would look to you - dreams have the power to change anything as in dreams the visual and the feeling (and sounds, and knowledge and such) do not need to be anyhow related.
(I had lot of dreams, where I died, but it was just interesting, no fear was there. And I had a dream of a big matchstick - it did not anything, there was no risk of fire from it, nothing, but I was scared to the bones and could not even work out why. Also I had really nice dreams about music - and I did hear all the tones as different kinds of blue color - visual and hearing simply switched place. Dreams are just like that sometimes - put unrelated (sensoric and/or emotional) labels on unrelated (dreamed) inputs without any logic).
There are also other things, that can help send nightmares away, but those are individual. The common is for her to believe, that it works. (As the nightmare is just a play of her mind, another play of the mind is able to fight it.) For some people "small rituals" work, but maybe even better is, if there is a "hero", who she can call for help and the "hero" would save her for sure. It may be some fairy, or her loved doll (which is awake at night and fights skeletons for her with magic), it can be a wooden sword or a shield near bed (well mainly for boys, but who knows), or the ability to magically summon an item in dreams and be sure, that it would protect her from anything. Magical rod, princess robe, unicorn, old teddy bear ... just say the magic formula in you dream and it would come and protect you from anything.
(Well the trick is to believe it and to say the formula - because if she can say the formula, she is able break the nightmare - that is, how it works. If she has something like that, she can use it in her dreams (but she would probably not remember it, while having a nightmare) or when she wakes up, you can tell her to use it and then you together summon the "hero" or the "artifact" and it will do its work. When you call it together, it would work for sure, because she would be fighting the nightmare with an even more powerfull spell (it is kind of self-fulfilling prophecy).
Bad dreams just happen. Really bad dreams are terribly realistic, while they last and even some time after. Sometimes there is a "clear reason" for such dreams (if something bad happened in real life), sometimes it is just touch of illness or bad food, or being tired or stressed and sometimes there is no reason to be found at all.
Really good is, that she did go to you for help (so she likes you and trusts you to help her) and that you really helped her.
If she will not have nightmares too often for long time, I would not think, that there is something bad. When a human grows, its body and mind are changing, sometimes really fast and at school age it is clearly visible. Also there is a lot of new information and whole big world around that she cannot fully understand (nor anybody else) and it brings a lot of insecurities. Somebody will react more visibly, somebody keeps it inside, but that is really individual and everybody has to go through this phase of life - adventures all around, but also insecurities and dangers.
She will have probably more nightmares in her life (we all have them from time to time), but she has somebody to help her and it is you :)