Voltage at UART Tx and Rx pins with no connections
Tx: Transmit

A stop bit (and therefore an inactive UART Tx pin) is high by default. So the voltage on that pin will be somewhere near Vcc when unloaded and when no data is sent out of the chip.

Rx: Receive

Rx is an input and therefore carries no voltage. Depening on the input circuitry of the chip the input may be pulled low, high or floating high impedance. In either case it can barely source/sink any current.