Most snakes will breed without brumation. The things that brumation do are:
1. Trigger better sperm production in males
2. Trigger a stronger breeding response in males and females
As I said, most snakes will breed without brumation, but brumation makes for more consistent breeding and more consistent SUCCESSFUL breeding, and a higher percentage of fertile eggs on average per clutch.
Photoperiod is probably the most important part of the brumation process, but the change in temperatures helps to trigger the biological responses also.
For some snakes, brumation will serve as sort of a "system reset", too. I've had snakes that were problem feeders, I put them through brumation and when they woke up in the spring, they were voracious eaters.
Some snakes you do NOT want to brumate. One example is any Drymarchon. If you put something like a Cribo down for the winter like you would a kingsnake, you will find a dead snake in the spring.
In general, the snakes that you are most likely to succeed in breeding without brumation are the tropical species, such as tropical milk snakes. You do need to vary photoperiod, night drop and humidity to match the seasons where they come from.