If you can keep your smoker at room temperature or a little lower, which is considered 68 - 70°F, and you move the turkey directly from the refrigerator to the smoker, cold smoking for an hour or two will be alright - but no longer then that.
As Saber pointed out, your better option would be to use a temperature of 200 - 225°F, for 2 - 3 hours and then directly into the fryer. You will probably obtain a better smoke flavor.
Either way, if you have a wire vertical turkey roaster, I would use one of those while applying the smoke so that more smoke and enter the cavity area. Most turkey fryers come with a stand to set your turkey on. So maybe that can be used as the vertical roaster.