Welcome to Jeepz.com . Not knowing the maintenance record to date , I would like to suggest a transfer case and front axle flush and refill with the proper lubricant . You could splurge and refill with Redline MT90 , but let's first diagnose the problem before putting more money first. I would also like to say that a full inspection of the front axle should be performed but realizing the weather is not in your favor that will have to be done when it suits you best . Will you perform the work yourself or have it done will decide that. Items to look for are wheel bearings , axle universal joints and an inspection of the ring and pinion and bearings while the inspection cover is off when flushing the front axle. I could go on and recommend inspection of upper and lower ball joints , steering linkage , brake lines but the situation at hands mandates a better day , like spring. But for now , it sounds to me like the transfer case is sluggish and it is likely the front axle lubricant is as well. Most important for the moment is to be certain the level of lubricant of the transfer case and front axle ( both axles for that matter) be checked. Also , be sure the front drive shaft ( rear drive shaft as well) are in good working order . Check the universal joints , grease them , replace them if necessary. A rear drive shaft u-joint letting go at the wrong time is very bad. A front u-joint letting go at the wrong time is DISASTEROUS ! Just imagine your oil pan being torn up for example. Please have at least the transfer case and both axles and all u-joints checked and if necessary , serviced. Please also check your transmission fluid level and fluid condition. As you know , the snow and ice will torture test your jeep as a whole and the four wheel system in particular. It's a chain reaction ; bad axle u-joints can blow up under stress , bad front shaft u-joints can cause a horror story , slipping trans will do you in financially not to mention hardship . Any one of the recommended checks is equally important but some are just more disasterous if luck turns bad. If I had to place a priority , t-case , trans , ENGINE , and axle(s) fluid level(s) AND u-joints . It sucks doing this work now , but I don't want to see anyone destroy their vehicle when they need it the most. Unfortunately , $$ dictates how dependable a vehicle is. Jeeps are no exception.
Note : when flushing t-case , FIRST make sure you can remove the FILL plug. If the fill,plug cannot be opened , you are stuck with NO lubricant If you drain it first. When jeep begins to become notably sluggish at first sign , check the front hub bearings for excessive heat and if one side is hotter than the other.
