Besides doing the taming via giving her meat, you can also:
1) Kill Ted, who appears during Day 1, and leave Snowflake in the Casino
2) Come back after 2:00 PM on Day 1 (before case 2-1)
3) Snowflake will join you with no hassle
Now that she's with you, stay away from the Safe Room. She will enter the vent with you regardless of how far she is from the entrance. Same with any other door.
After this, the easiest psychopath to encounter will be the "motorcycle-riding psychopath" found in Fortune Park during the mission "People Like Us". Look for his Slicecycle near the maintenance room between the Uranus Zone and Atlantica Casino entrances.
Now, the hard part is getting Snowflake to maul the psycho. She tends to like eating zombies over crazed motorcyclists. So, try clearing out an area of zombies (usually where the fight starts works), get him stuck on a wall by jumping out of the way as he comes at you, and hope she gets him. Shouldn't be too hard.