I replaced the Coleman thermostat several years ago with a residential and if your Four Winds is like my Four Winds and the thermostat wiring followed the standard color coding you could try to force the A/C on with jumpers to bypassing the thermostat and verify the A/C is responding correctly to calls for blower and cooling.
What you should see at the thermostat is -
Red wire to the R terminal which will be 12VDC from the furnace via the A/C.
Yellow wire to the Y terminal which will turn on the A/C compressor
White wire to the W terminal which will turn on the furnace
Green wire to the G terminal which will turn on the A/C blower
There might be a fifth wire which is used to set the blower speed to low. I can't recall the color but a residential thermostat normally does not have the blower high/low speed function.
Jumper R to any of the terminals will turn on the associated function. If not you will need to trace the lines to see how your system is set up. Normally when the thermostat calls for cooling it will set for both Y and G with 12VDC to turn on the function. If the wiring is correct and everything works as expected by jumping then maybe the thermostat isn't happy with something.
Also if you have a thermostat that will automatically switch between heating and cooling (what I have) ensure you have if programmed so the two functions do not over lap and are separated by a couple of degrees. In other words if your minimum temp for A/C is set to 70 then set the maximum temp for heat no higher than 68 or so. A few degrees of separation is needed as the switching action of the thermostat isn't exact.
I am 39 years short of being 100 years old, a retired sailor but prefer two wheel racing with a both left and right turns on the race course.