My experience as a teacher of English as a foreign language has taught me that how to use ‘have to’ and ‘must’ causes quite a few problems, so here is a quick guide on the subject. I usually break it down as follows:

Use ‘have to’ for outside forces:
I have to go and visit the doctor, I have really bad mouse arm and it’s keeping me awake at night.
If I am to get to work on time, I have to set out at eight o’clock.
I only use my car when I have to, usually when I have to teach in another area.
I have to wear smart clothes at work, it’s company policy.
It’s raining so hard that I’ll have to take the bus.

Use ‘must’ for inside forces, like your own feelings:
I really must lose weight! I look like a pear.
I must rush. I’d like to get to work early so that I can leave early too.
I must use my bike more and leave the car at home. I don’t get enough exercise.
I must buy some new shirts; these are looking rather shabby.

The opposite of ‘have to’ is ‘don’t have to’:
I don’t have to get up early tomorrow, I got the morning off.
I don’t have to shave at the weekends, because I don’t have to work.
According to the tax office, we don’t have to charge VAT on handicrafts and second-hand goods.
You don’t have to spend lots of money to have a relaxing holiday.

‘Must’ does not have an opposite, so use ‘don’t have to’ instead.

‘Must not’ (mustn’t) has a different meaning, similar to ‘cannot’ (can’t), is usually quite strong and refers to rules and regulations etc:
You must not carry sharp objects or large amounts of liquid in your carry-on luggage.
Motorcycle helmets must not be worn when visiting the bank.
You must not take photos here, it is a top security area.
You must not buy or sell pirated videos.

So, in summary:
I have to lose weight, the doctor said so.
I must lose weight, I feel unattractive.
I don’t have to lose weight because I’m underweight already.
I mustn’t lose weight – the European Union has standardised the human body!