Walleye is a Fish caught when raining in fall and can be found in Rivers, Lakes, and the Forest Pond (Forest Pond needs confirmation).
Livin' off the Land states that it can be found at fall and winter on rainy evenings in any freshwater location (Rivers and Lakes).
It claims winter and fall but further research suggests they can only be caught during the fall. It is suspected a bug is preventing catches during winter. This is likely due to snow not being considered rain.