You can ‘get a short haircut’ if you’re talking about going to the barber. I’m going to get a short haircut this time. Otherwise, natural are things like: I’ve decided to wear my hair short. I keep my hair short in the summer. She’s going to try short hair for awhile. Do I look good with short hair? But ‘having a short haircut’ is possible too. I’ll have a short haircut in August because it’s required by my new job which I start in July. (The context is that people understand that your current long hair isn’t compatible with the job you’re going to start. But I’d still probably just say ‘I’ll have short hair’)

You could also say It's been so hot lately I decided to get my hair cut short. But even more natural I would say It's been so hot I decided to cut my hair short(it being understood already I went to get someone to cut my hair and didn't cut it myself)