"have some refreshment" is correct and usable in written English.
You could use it in a sentence like, "Would you like to have some refreshment while you wait?".
Gavin B. Keilly's GBK Productions held court at the clubhouse with its George Lopez Gold Classic Gift Lounge where celebs could relax, have some refreshments and pick up some goodies.
Have some refreshments available, let people sit comfortably.
You can have some refreshments at the Zhilmil Dhaba near Murthal for special stuffed tandoori parathas and lassi.
You will pass by a Salon, where you can have some refreshments at Cafe 7, Paragon and Himalayan Coffee House.
Keep driving for more 53 kilometers (33 mi) on NH 22 to reach Chail, you will pass by Chandigarh where you can have some refreshments.
The girls wee not there but later, they came over to the Drake Hotel, where the two men were having some refreshment.
Or come in the evening with a date, and bring some refreshment -- have some fun and make some art!
Pop-up refreshment stands have some history here, as well.
After the event we'll be having some networking with some refreshments and finger food in the same location.
Some have offered refreshments or had their choirs serenade the runners and the crowds.
