Can Timer B be clocked with an external clock while in LPM3 mode?

Yes, Timer B can still be clocked externally when the CPU is in LPM3.  You can configure an external pin to be TBCLK, and then you can configure Timer B to run from that clock.

I have found MSP430 to be extremely versatile in spite of its low energy consumption.  I especially like the x5xx family.  Good luck to you.

Jeff

Both timers can be set to an external clock and clocked while in LPM3.
But if it is this external clock you want to measure, you'll need a reference timebase, which has to come either from inside (crystal, REF oscillator etc.) or you need to provide an external stabel clocking base and need to capture the frequency using the CCR units.

Let's say you have a stable precision 1Hz clock signal and a higher-frequency  signal you want to measure (up to 65kHz), you can clock the timer with this signal and route the 1Hz signal to a CCR unit. Whenever the 1Hz signal comes, the current count of the timer is captured and an interrupt is generated. The difference between the captures timer coiunt and the on from the last1Hz trigger gives your frequency. During this, the processor can stay almost all the time in LPM, is awakened once a second, does some subtraction and outputs the result to somewhere and then goes back to sleep again.
Keep in mind that waking up from LPM takes some µs and getting a crystal back to work which was switched of during LPM (e.g. for clockign a serial connection) takes even longer.

If you don't need full processing power all the time, the MSP is the best you can get for low-power consumption applications.