It depends on the county. Custer County natural gas, LPG and electric grills are allowed.
Natural gas, LPG and electric "grills" aren't grillin, just cookin outside. Charcoal FTW!
Anyway, here's a link to the forrestry website. Just click on your county and it'll have the specific language for the ban in said county.
http://www.forestry.ok.gov/burn-ban-information