It would be better to say that you should choose your socks according to the color of your pants

Hi, Zhanibek! "Have to" and "must" are actually synonyms, so either word is fine. It's just a matter of how each "sounds" in any specific context; in this case, both words are okay and come across the same way. Thus, your sentence can read: "You have to/must remember that you should put your socks on according to your trousers' colour." Make sure you add the possessive apostrophe after "trousers." I hope my answer helps! =)

You could use either "must" or "have to" in that sentence. There is no difference in meaning here. There are other problems with the sentence, however. "Put on" is not the right verb : "put on" refers to the act of dressing, not of choosing what to wear. I agree with Tyler that "choose" would be a better verb. Another problem with your sentence is the last three words. "Your trousers colour" (even with the apostrophe which Mr Zhang correctly suggests) is not natural English. It should be "...the colour of your trousers". Also note that while "the color of your pants", as Tyler suggests, would be fine in an American context, it could be confusing elsewhere. For English speakers outside N. America, 'pants' means underwear.

You could have used any of them depending on the situation. Both of them are used to express obligation; however, "have to" shows us that the obligation comes from somebody else. It’s a law or a rule and the speaker can’t change it while "must" shows us that the obligation comes from the speaker. It isn’t a law or a rule.