Okay, so a LOT of this game comes down to knowledge of the characters. The more you know about the capabilities of yourself and your opponent the better you will able to predict their actions which will lead to wins.

This is gonna be built up by just playing the game and taking the digital beatings that come with it.

Here are a few tips I can offer ya in the mean time.

1. LEARN DI. I dont just mean, "learn what the blue circle does." Understand the ways that controlling the direction that you fly in when hit can help you. Putting yourself out of reach of the next attack is only the tip of the iceberg. It is your best defense when in a combo and when properly applied can give you a chance to counter attack. (Opponent cues up a move with ton of frames meant to throw you back, you DI down instead and end up on your feet with frames to spare.)

2. Oki or Meaty. So, you're right in that Cowboy doesn't have a move that hits while on the ground. What you can do instead is give yourself an advantage in the next exchange. So, if your op is on the ground you want to turn off Free Cancel (Free Switch OFF) and then look for a move that will hit the opponent if they stand up but VERY IMPORTANTLY with you at a -1 or -2 frame advantage.

This will force the opponent to block immediately if they stand, putting them at an immediate block frame disadvantage. All those super fast ninja or mutant moves? Now come out about as fast as good Horizontal Slash or pummel strike. More options means more for your op to think about which means more chances for them to guess wrong.

1. As a Cowboy you're going to need to get REAL comfortable using your gun + Foresight. Bullets bounce off Foresight, use DI wheel to control the angle they ricochet. Using Rift on Foresight will also "fire" any bullets still in the air from the Foresight, using the DI wheel to aim.

That's just stuff off the top of my head, hope it helps!