Hey there sirotanchelly! I've done two HP scarves, and I can tell you, it's best to cut the yarn. You can leave a nice tail on the inside of the scarf (I assume you're knitting in the round?), and after you weave in the ends, the tails will be on the inside and no one will know.
If you need a pattern, I used this one.
Also, there's a HP Scarf Knit-Along on this lovely message board, you can check it out here