Gas water heater vent too short?

I had a vent that stood about 3' above my roof that used to service both my furnace and gas hot water heater. I had the furnace changed several years back with it's own venting. I just had my roof redone and asked if he could cut down the vent pipe and change out the ugly, old cap. I didn't question much as I thought he would know what the height requirements were. I was surprised when he cut the vent within 1" of the roof line and put a 4" standard flue on it. I envisioned a shorter vent with a newer cap. The new vent is below the highest point of the roof ridge. The roof ridge is about 1 1/2 feet away.

I know it vents as I've lit a match, blown it out, and the smoke goes up the vent.

I'm also concerned about snow as I live in Michigan and the vent would certainly be covered in the winter, although I assume the snow around it would melt?

Are there specific guidelines on how high a lone gas water heater vent should be?

I like the looks of the new vent, but I want to be safe and be within building requirements. Thanks.