Right there may be your biggest problem. I charge and store my batteries inside the house. That way they are warm before I begin and the heat generated by the discharge keeps them warm enough so that I don't have run problems. You are dipping a bit into the cold end of the pool for optimal battery range but starting cold makes the problem worse.

I also always charge my batteries after use. That way the battery is always a full charge and I don't have to guess if I have enough light to get home. Li-ion doesn't need to be cycled like NiMH or NiCd needed to be so topping up the charge isn't as much of a problem.

Finally, alkaline batteries seem to be unaffected by the cold. I use alkaline for my taillights which are stored out in the cold. Never had a problem with them. Granted they are disposable but a set of batteries will a year or more per light so I don't feel like I'm destroying the planet by using them.