In a laboratory setting or in an indoor aquaculture setting where you can manipulate water temp and photoperiod, you can get Walleye to spawn every month of the year. Not the same females and males though. My wag would be that each fish could only spawn once a year.
I believe this to be true of perch , walleye and sauger as they have to go through a thermal cycle for eggs to properly develop.
The cold side is what matters most.