First and foremost - you do have plenty of washer fluid, and not water in the resevoir?
Water will freeze. An easy thing to overlook. (Not that I have done it
A haynes or owners manual should locate the fuse. It may be in some obscure place...
On my lesabre there are fuses under the driver side, up in the dash on the right, and more fuses under the hood (really huge ones)
Find and Check the fuse, just to get that out of the way...now for the fun stuff
Is the motor electrical connector hooked to the motor?
You could test the motor by hooking it directly to the battery and you will hear it work (or not)
ALSO, if you have a multimeter, hook it up to the fluid pump electric connector, and have someone operate the switch on the turn signal arm. You should read about 12 to 15 volts.
You will now know if the motor is bad or if it is not getting power.
If the motor works but the plug is not feeding voltage, there is a wiring problem.
But do those checks first. Don't buy parts yet unless you really need to.