The first time I had a cold war with my husband, the first time I refrained from looking for him, and he sent me a short message.

According to your description, your husband doesn't care about it at all.

In other words, your husband may know you too well.

Knowing that you will come back eventually

Otherwise, he wouldn't send such a short message.

If he is nervous, he will coax you back.

In other words, your husband has a crush on you and thinks that even if he doesn't look for you, you will come back.

If you compromise again this time

I can't talk anymore.

Since it is a matter of principle, don't give in.

Make sure your husband understands your position.

If he is nervous and you are afraid to leave, he will come to you on his own initiative.

If he really doesn't care about you leaving,

I don't think you'll miss anything.