Is it correct to say ' I will get a hair cut today'?
Is it correct to say ' I will get a haircut today'? or (hair cut?)
It is wrong to say ' I will cut my hair today' right?

Thanks a lot for your help in advance. Have a nice day!
Hyunwook

Question

Is it correct to say ' I will get a hair cut today'?
Is it correct to say ' I will get a haircut today'? or (hair cut?) 
It is wrong to say ' I will cut my hair today' right?

Thanks a lot for your help in advance. Have a nice day! 
Hyunwook

Answer

"I will get a haircut today" means that someone will cut your hair for you.
"I will cut my hair" implies that you will do it yourself.

Answer

'I will get a haircut today' is correct (you will go to a hairdressers and they will cut your hair.)
OR
'I will get my hair cut today' (notice the difference, 'haircut' is a noun, whereas in this sentence you are using 'cut' as a verb.)

'I will cut my hair' is a correct sentence, but it means that YOU will cut your own hair. I think it's unlikely that you mean that.