A belt will slip when you first "dress" it,it gets tacky as it dries,how old is your battery?i would say it may be getting weak,as stated an alternator usually just quits.The gauge in the dash is measuring volts in the battery,it is probably running off the alternator once you start driving and it is holding a little charge.if it is a serp belt with a spring loaded idler it can't be too tight i wouldn't think.You will need an amp meter to check the alternator.If it sets a couple days it will probably not start.cold weather is a battery salesmans dream.
the belt being sticky is what the noise is probably