AX2550he to control series wound motor

Will the ax2550he operate a 4hp series wound golf cart motor?

If it is only one motor, then you should order the AX2550HESC (single channel version) and there would be no problem.

I'm going to run two motors in the tank mode.

Yes it will.
If you need to connect to only one motor, you should order the single channel version ax2450hesc

The motor I'm looking at is a reversible golf cart motor with four post. A1. A2. S1. S2. Will it work or do I have to get a two post motor.

if you want to be able to control the motor in forward and reverse, you must be able to apply a voltage on S1 and S2 whose polarity can be reversed. Polarity on A1 and A2 can remain the same.
We have a product that is specifically designed for these kind of motors. See dev.roboteq.com/dev1/separate-excitation...tor-controllers.html
To be certain, you should measure how many ohms you have between S1 and S2 and let us know the value.