Is this an effective solution for freezing pipes?

It can, but only if the section of pipes that freeze are in the direct circulatory flow of the pump. A branch line not in the flow can still freeze.

After a really bad cold snap here with temperatures down to around 19 this pump kept all the pipes above freezing. That is a nice side effect for sure.

I think so if the temperatures aren't well below freezing for long periods of time. Insulating the hot water line would be the first line of defense against freezing. keeping the water moving would then be more effective.

It's partially effective. It will prevent the hot/cold water pipes to your sink from freezing. However, the cold water supply from the main will have no flow in it. If that pipe is in a basement or another warm location, it will be OK. If it's in a cold crawl space, you'd better leave a faucet running. In my installation, I leave the kitchen faucet dripping at night when it's very cold. But it's no longer necessary for me to leave the bathroom faucet dripping.