The HART signal will probably have good frequency accuracy as the HART modem chips (such as the Maxim DS8500) will use a stable oscillator, and guarantee phase continuity. The electrical environment that of a HART connection will be industrial and noisy, so you will need proper filtering in the analogue domain so that the noise doesn't swamp the ADC input range. I would also suggest increasing the ADC sampling rate to make the design of the nyquist filter easier.

Detecting a frequency in a set of digital samples is a textbook DSP problem.