Not really- the snort means “I feel awesome” and a stallion is trying to convey his status, not his weakness, so he’s going to snort to express how awesome and fit he is. But stallions in a territorial mood don’t just snort, they add a lot of other signals, too. He’s saying “get out of here” by pawing the ground. Done at the same time it means “Get out of here because I am awesome and I am going to bite and kick the s#!t out of you if you don’t.”
People grin because they feel good, but people who grin while cracking their knuckles, puffing their chests out, and putting their feet in a wide stance, etc., are sending a stronger message not unlike the stallion.
When horses snort, they are up to something. Stallions sure aren’t being friendly when they snort. Other horses snort when they are running and playing. If you are on a horse or have one in hand and they start snorting it usually means they are fixin to have a come a part.
I've been around plenty of stallions. Snorting to them is a sign of aggression. Never said anything about being a weakness. Their most aggressive posture is rearing to try and gain an advantage over a rival or countering a threat. But snorting is one of their ways to clear their path (or their nostrils).
He’s saying “get out of here” by pawing the ground.
All horses hoof the ground, and for various reasons. When they are in their stalls, in cross-ties, or awaiting food in a paddock. Most do so out of boredom.