I have a lot of copper tubing from the utility room to the refrigerater
Ice maker. A lot of room to install a water filter to the ice maker. The thing is should I install the filter after the saddle valve, or before the saddle valve. I think it should be before?

Your saddle valve takes off from the faucet supply. To install before the saddle valve would be to cut into the supply and that's not practical if you wish to filter your ice cubes. Install the filter where it will do the most good. After the saddle valve, good luck, Tom