I would consider that intermediate if you feel very well balanced in the saddle and have good control over the horse. I do not consider myself beginner-intermediate, but lower-ish intermediate. I've been riding for 2 summers and one year, and I am able do the same things as you, minus the cross country jumps, riding in fields... and I've never fallen (thank god ><). The highest I jumped was... one foot?
So yes I think you have the right to call yourself an intermediate rider. :))