Second conditional when making plans for the future: "If it rained tomorrow, I would go to the cinema."

You could say

If it doesn't rain tomorrow, I will go to school.

or, more pompously,

If it weren't to rain tomorrow, I would go to school.

The problem is, you're mixing past and future conditions. In both cases, it can't have rained tomorrow.

It depends on how likely the conditional event is, or how likely you would like to portray it as.

For a conditional clause expressing a possible future event, you have two choices: (i) put the inflected verb in present form, or (ii) put the inflected verb in preterite form. Use option (ii) if the contemplated event is unlikely or being posed as if contrary to fact. Use of the preterite does not in such a case imply past tense (and it obviously couldn't, since we're talking about a future event), it is instead called the "modal preterite", since it is used for a non-indicative mood.

The second clause should have its inflected verb in the same form as the conditional clause does.

If it rains tomorrow, I will go to the cinema. (It is likely to rain tomorrow)
If it rained tomorrow, I would go to the cinema. (There is no reason to believe that it will rain tomorrow, but it just might happen)

I am not comfortable with the sentence "If it rained tomorrow, I would go to the cinema." "If it rained" speaks of a future event in the past tense, which is not logical. When hypothesizing about tomorrow, logic demands you use the present tense; for example, "If it rains tomorrow, I will go to the cinema" (or to show resoluteness or determination, I suppose you could say "If it rains tomorrow, I go to the cinema"). As for Robusto's "If it weren't to rain tomorrow, I would go to school," I can't wrap my head around the phrase "If it weren't to rain tomorrow," but then maybe I'm just a little thick!

Here's another variation on the theme: "If it rains tomorrow, I go to the cinema; if it doesn't, I go to school."

Use of both type I and type II is correct in this case, but with different meanings and applications. If you use the type I structure, as follows: "If it rains tomorrow, We may have to stay in." as is the case for other type I examples, you are referring to a real/possible situation in the future; However in case of using a type II structure in your example, which would be the following case, "If it didn't rain tomorrow, We could/would go out for a picnic."
you somehow know from somewhere, from the weather reports for instance, that it will rain tomorrow and therefore, a type II structure is used to refer to the unreal/imaginary situation in the present/future, which is why second conditional is used. to put everything in a nutshell, both type I and type II are possible, but with different meanings and applications.