WHen the temp goes below 35 outside the carrier heat pump cycles every minute. Is this caused by the thermostat or is there a relay to prevent the defrost from cycling at cold temps?

Regardless of what type of control you have the compressor should not be attempting a start every minute.
If you're running your heat pump in temps below 40 degrees, there will be more frequent defrost cycles but certainly not every minute.

I'd have a tech diagnose the sequence of operation because you are describing a problem that needs a competent tech.

I agree with aldematt57. The timmer board or sensor is probably defective if it is going into defrost that soon. It could also be the pressure switch and a few other different parts that is why alsematt57 said you need a professional to look over your system and make a proper diagnosis other wise you will spend big $$ just replacing all the parts till you find the defective one.