If it only says you can ride at short distances I would say no running. I noticed in your other post that you are losing weight, but until you have reached a size that is a little easier to carry I would stay away from running.
*sorry if I sound mean. I definitely do not mean it to be that way at all.
I am 6'8" and pretty close to 300 myself and I find that if I condition my horses and I don't try to ride one hard day after day my size has little effect on them. It also has alot to do with how well you ride. If you flop around like a bag of potatoes you will wear out and sore your horse faster. If you ride a quality saddle with quality pads and you ride well then you should be fine. Pay attention to your horse and let the horse tell you when it is struggleing.
May I suggest looking at the thread about taking your horse for a walk? Here: http://www.horseforum.com/trail-riding/taking-your-horse-walk-37485/ Maybe when you go out to "ride" for an hour, you start with 5 minutes on the horse, and the rest walking. Then increase the riding gradually as you learn what the horse can handle, and as you both gain condition and perhaps lose weight.
A horse can carry 25% of it's body weight successfully on a 50 mile endurance race. I weigh 193 plus saddle, blankets and water bottle or 220 pounds running weight. My guy weighed in at 870 pounds and we ran 35 successful endurnace races. I kept him to 50 milers because at 100 miles I would be too heavy.
He is now retired and carries a 250 pound rider, an older gentleman who rides easy. So a 870 pound horse can carry a 250 pound rider easily.
Your horse is heavier as is your weight but ride easy, find out if the horse has problems and go from there.