Did it sound thick when you played it? Easiest way to get a thick snare recording is to have a thick snare sound in the first place when you record. I like SM57's for really fat and dull snare sounds. But I hate those sounds, so I don't use them. And a million people are going to respond with generally what I said, just be forewarned.
Anyways, addressing your question, I've found a couple things thicken up the sound of the snare. First, do a high-Q (4+) peak boost and sweep slowly around the lows and low-mids. Most snares have a lot of body and depth around 100 - 200 Hz, depending on the tuning and size. When you find that frequency, turn off that peak boost and boost above it with a low-shelf and a medium-Q (.8) so that you are catching that frequency. I like
PSP MasterQ because it's easy to see what you're doing as well as hearing. Keep in mind that when you boost at a frequency, peak boosts and low-shelves act differently. That's why I recommend an EQ with a display.
Next, trap that low-frequency boost with a high-pass. I use a 24 db/octave and mid-Q (.75) and sweep up until I've found a nice spot. This cuts the unnecessary bass out but keeps that low-body boost in.
Finally, sweep around with high-Q peak boosts until you find nasty frequencies in the mids. Oftentimes, they will be multiples of that first low frequency that you found. Cut these with higher Q notches. This will allow the body and attack to come through.
Finally, compression will help. Play around with the attack times because too long will not tame the attack but too short can kill the attack. This can make the snare sound a little bigger. Some parallel compression (do a search) will also thicken up the drum sound.