[David L.]

The trouble we are having is that what is "correct" English is not always how we express things in casual, everyday speech.
"true of" implies that something has an intrinsic quality,or state, or condition
"true for " means that something about X can be generalized or also applied to Y.
So: say in my experience, lawyers always seem such serious people, even when they are not at work but home relaxing. Say that I have found that accountants are like this also. Then there seems to be some intrinsic personality feature of "seriousness" in people of these two professions. I might then say: "Lawyers are very serious-minded individuals, and that is true of accountants also." (My apologies to lawyers and accountants for this no doubt unfounded observation!)

In the first example you gave, you are not referring to some intrinsic quality of students, that all students are generally in some excitable state most of the time, such that it is a characteristic of students; but that they are feeling excited at the prospect of some coming event. So are the teachers. So, "..and it is true for the teachers also."
In your second example, it is an intrinsic feature of the climate in the northwest that they get a lot of rain. Cumbria is a part of the northwest. So, ..,and that is especially true for (that part of the northwest called) Cumbria."
Compare : The Gobi desert in China receives very little rain throughout the year. In England, this is also true of East Anglia.
With "lawful ", the word is characterized by being mainly used in technical and literary writings. The synonyms of "lawful" tend also be characterized by being mainly used in technical and literary writings. So, "it is also true of the opposites."
However, you will often hear people saying "true for" in both situations, as "true of" to modern ears sounds rather 'correct' and 'formal' when people of just speaking casually.