problems with Battery not even 1yr old

i have a 91 sunbird 2.0l tbi i had replaced alternator and battery last jan. lately we have had some cold weather here in green bay wisconsin and lately i have had problems with my battery. when i get home from drivcing some place and put my brakes on in the driveway to put the car in park my idledrops to like 400 rpm. yesterday we had gotten 5 in. of snow and whild i was driving and putting my trun signals on my spedometer needle would jump up and down and with my turn signal on and i would apply my brakes my oil light would come on. so im dring to my friends house and would look at my gauges and they seemed a little dimmer than normal. my car seemed to be running fine. then 2 hrs. later i try to start my car and my battery was dead. my friend and i let the bat. sit on charger overnight and when we get up in the morning it turns over fine then when im dring home the turn signal thing happens when turning. im thinking analternator problem. i dont have time to check it but does this sound like it could be the problem?