'I'm seeing her at 10'. This is a classic textbook example of the use of the present continuous for future arrangements. If you have a fixed appointment, you use the present continuous. A native speaker would never use a 'will' future to refer to an appointment that is already in a schedule. Here's an example of a natural use of 'will': Hello. Can I make an appointment to see Dr Brown? Yes, certainly. When would you like to come? Tomorrow afternoon if possible. She doesn't have any appointments free in the afternoon. We can do 10 o'clock or 11.30. OK. I'll see her at 10. In this case, you use 'will' because you are making the decision at that moment. Later on, you'd tell someone else that you 'are seeing' the doctor at 10.

Both are perfectly valid. Native speakers use either phrase.