Does Honeywell make a system that can call you on your phone if your furnace goes out in the winter or any other company ?

Your alarm ( or a alarm company) can have it set so if the temp in your home goes lower than a present temp, it will either notify you, or notify the monitoring company who will call you.

I have had those in several of my old work places.

You could try Sensaphone, or a U.S.P. Dialer, it calls you directly, no monthly.
If you have a Ademco/Honeywell Panel and is monitored, you could add this to your sone list.
I did it before on an Ademco with their thermostat and a remote board(I forget the exact name) can get tje number for you if you choose this route.