I thinkg the tense is awkward for the party meaning. Unless "We have a barbecue in the garden every year to celebrate the start of summer." Or something that shows habit.
Yes it's not something you would just say out of the blue. It would be a habitual barbecue of some sort. 'What do you do for your birthday?' 'We have a barbecue in the garden'.
If it's a one-off you would say 'We are having a barbecue in the garden'.