I have a shutoff valve on the cold side of the water heater inlet. I also have a water main shutoff valve coming from my well. Are the cold and hot water lines in the house independent of each other and can I leave the main water valve open and just shut off the valve on the inlet side of the tank, therefore allowing me to drain the tank while still having water to the cold side of the house?
Yes they are completely separate, from some point after the source (in your case, your well) and before your hot water heater.
If you turn off the valve at the well it turns off all the water to the house, both cold and hot
If you leave the value open at the well and turn off the valve at the hot water heater, then the hot water will be turned off and the cold water will remain on.