Frequency Domain Distribution
I assume you mean that at each time $t$, the signal is a normally-distributed random variable.  This tells you the probability that the signal will take a value in any given range, but it does not tell you whether/how the signal values at different times are related to one another.  Typically, for a random signal one defines not only the probability distribution for the signal at each time, but also the autocorrelation function $E \{ x(t) x(u) \}$ or some other measure of how signal values at different times are related or independent.  This is required in order to determine how the signal is distributed in the frequency domain.