The difference between Forward and Reverse in a series motor is the direction of current flow in the Stator windings.
(While either way is technically correct, the stationary windings in Series motor are typically called the Stator and in a Sepex motor they are called the Field)
Here is a drawing of a generic series motor set up.
As you see, the Stator current flows from left to right with the F/R switch in one position and from right to left with the F/R switch in the other position.
Basically, current flows A1 -> A2 -> S1 -> S2 for one direction and A1 -> A2 -> S2 -> S1 for the other.
If you can come up with a way to switch the cables connected to S1 & S2, your in the snow blowing business.
