Does anyone know why my compressor is making a lot of noise after I installed a new hunter touchscreen thermostat? Please help!

Are you sure it wired right? Could it be the reversing valve making the noise? woops assuming you have a heatpump. If not and if you have air only condenser unit, and unless it pretty warm, the compressor shouldn`t be started up in the winter,the compressor might be flooded with most of the freon migrated to the condenser unit which makes it a no-no to start the compressor.

If you do have a heatpump you may just be hearing it go into a defrost mode. Its hard to say with out knowing if it's a heatpump or what, are you in cooling or heating mode? Did you change the thermostat because system was not working right? We need more info if we can get it.