For example, I play nightmares to the Red Keep, and play frozen solid to it, and what will happen when this phase ends? And please tell me why. Thank you.

Frozen Solid would remain attached because it's creating a continuous blanking effect at that point.

The sequence of checks goes like this:

1. Card in natural state (text active) = "No attachments" : Prevents Frozen Solid from being attached
2. Card in natural state (text active) - Nightmares (text blank) = Text blank : "No attachments" invalid, Frozen Solid can be attached.
3. Card in natural state (text active) - Nightmares (text blank) - Frozen Solid (text blank) = Text ( really ) blank : "No attachments" invalid.
4. Card in natural state (text active) - Frozen Solid (text blank) = Text blank : "No attachments" (still) invalid.

Effectively, because there is still a valid "text blank" effect at the time, the location's text does not come back when Nightmares wears off.

Just because the result (Frozen Solid on the "No attachments" location) would have been impossible to achieve without Nightmares is no reason to think that the situation is illegal once Nightmares wears off. The order of effects can matter a lot in games like this.