Some well water testing companies suggest annual or twice yearly testing of well water. I don’t think that testing annually is the factor to be thinking about. Rather, I would test your well water at the extremes of weather, meaning during wet times versus dry times, and before and after any major construction such as a new neighbor drilling a well or a nearby fracking operations.
In my experience well water can become much harder (meaning it contains more minerals) during times of drought. The well may be pulling water from lower portions of the underground aquifer or water that has been there longer and had more time to dissolve minerals from surrounding rock.
And water can become much fresher after periods of substantial rain. Yet I have also seen levels of iron in well water increase four fold after heavy rains. Apparently the iron is captured by rainwater as it descends through the ground above the aquifer.
If there is farming near where you live you may wish to test for pesticides in well water. Doing so in the winter makes no sense to me. I would test for pesticides after farmers have applied them in the late spring. Once the farmers apply the pesticides wait for rain to carry them into the local aquifer. Wait another week or two and then test your well water. This is when they ought to be at the highest levels.
A new neighbor who digs a well can tap into the same aquifer you’re using and this may affect your water by beginning to withdraw water from the aquifer at a higher rate. Likewise construction or fracking that that alters the geologic featurs that contain your aquifer may affect water quality. In this case you want to test your well water before an operation like this starts then again afterwards. Be sure to allow some time between tests.
One problem with well water testing is that you may gain a false sense of confidence. A water test is a glimpse into the well. Only frequent testing at the points of extremes in weather or conditions will provide you with a sense of the range in water quality within your well.