Snodin said: "We could have drawn a non-League side, but at least we know what Oldham are about and what we have to expect. Hopefully we can go there and put a performance on.
"They are a hard-working side. I know Dave Penney very well and they will be up for it. It will be tough, but hopefully we can get closer to that third round draw."
Leeds have failed to reach the third round on both occasions since relegation from the Championship two seasons ago, losing to Hereford in a first-round replay at Elland Road in 1997 and famously falling victim to non-League Histon last season.
Snodin added: "We want to win that game on Saturday and keep the winning habits. It's a great cup to be in. It goes all around the world. I played in the semi-final for Sheffield Wednesday against Everton and it was a great day, but we lost and there were grown men crying in the dressing room afterwards."