There can be many reasons why a snare doesn't sound good. But if you're having real problems getting the drum to sound good, severe EQ is probably the last thing you should use. Better to change mic, move it, or change the drum itself. Do understand the challenge you’re facing is not only dealing with your skills, but with the drummer and their ability to make a good sound. I was told this was true early on in my career, that the biggest part of the sound is due to the player, but I never realized how true it was until I was recording a session where a drummer was swapped mid-session.
I was recording a commercial session for a theme park and knew we’d have two drummers for the date, as the first would have to leave early. I’d recorded the first drummer many times before and had never really been happy with the results. But I was a young engineer; as these were commercial sessions and I never had the time I would have on a record date, I concluded the lesser results were mostly due to the lack of time. We had decent, but not great drum sounds. When the new drummer arrived, I asked him to play a bit to simply check his levels. When he played, the entire drum kit lit up and sounded IMMEDIATELY better! I was stunned. It was so much better the producer jumped up off the back couch and asked, “What did you do to the drums?” “Nothing!” I said. “Just hire HIM next time!”
All this to say, when you’re dealing with difficult drum sounds, you have not only your abilities, but the studio, the gear, and also the drummer to deal with. And while you probably can’t change drummers, you must understand their role and when needed, take steps to help them make better sounds.
One huge misconception for drummers who are new to the studio is that they think they need to hit their drums hard to sound good. It's especially common for drummers who’ve played live most of their career. The fact is often the opposite. The harder the drums are hit in a studio, the more choked they sound. Medium-hard hits often do all that’s needed. So if you’re having trouble with drum sounds, go out and listen to the drummer in the studio and find out if they’re hitting really hard. If they are, remind them they don’t need to do that as you have all these mics right near the drums. It's like a close up in film.
This can be very hard for some drummers to do, but it may be what’s needed. You'll need to listen and see how they react to your comment. If they can't do it without losing feel, then you'll need to tell them to go back and hit harder, and find some way to make it work. Feel and performance trumps sound.
But as the engineer, it's your job to take charge. You must thread the needle to help your players give not only good musical performances, but good sonic results.