Planning to use your generator during the winter? If so, consider changing to a lower weight oil. The oil weight determined by your local temperatures. As was noted by others, periodic operation of the generator is the recommendation of the manufacturer.
At the local auto store I found a very inexpensive thermometer which included an outside sensor. Easy to hide the wiring along interior molding. Used velcro to affix the thermometer to a shelf board, where it is easy to view. One AAA battery needed, which last for years. Thermometer can be set to sound an alarm at 32f.
You can give yourself a bit of a temperature edge with your water heater if you use mailing envelopes as insulation. Cheap, available, and can be sized to fit. (Remember to remove before using the water heater). Note attached image.