The tube has a lot of surface area and not a lot of volume, so it's going to lose heat quickly compared to the reservoir. In addition to insulating the tube mentioned by Glenn Gervais you can start with hot water in the reservoir and frequently drink a little bit to keep reheating the tube. This Nordic skiing article discusses this technique in more detail.
You could also try a Nordic skiing water bottle holder like the one in this (5 part!) article. I've noticed while skiing that a horizontal bottle seems stay ice free at the valve longer. In a vertical holder, turning the bottle upside down also helps.
I've never tried this, but you might also try to keep the water in the reservoir warm by attaching a chemical hand/foot warmer to the outside of the bag. Test it first to check that it won't damage the plastic bag, though I wouldn't expect something made to keep near your skin would get hot enough. Don't put it in the bag though. If it leaks it's probably dangerous to your health.