There has long been a sentiment among producers that in cold years, calf birth weights are increased. There are many inherent challenges in proving whether this is actually true. Differences in bull as well as nutrition are the biggest hurdles.
Research that evaluates this question is limiting. However, one study conducted by researchers in Nebraska during the 90's attempted to follow birth weight and dystocia as impacted by winter weather (Deutscher et al., 1999). For six years, March calving heifers (of similar breeding, similarly bred) were evaluated. The trial did show birth weights and dystocia were the greatest in the coldest years. The coldest winter during the study was an 11 degree Fahrenheit difference from normal. This resulted in an increase of 11 pounds in calf birth weight. Calving difficulty increased as well.
The theory behind this is that during cold temperatures cows shift blood flow from the extremities to major internal organs. This results in greater blood flow to the fetus. In turn, more nutrients are also delivered to the fetus... increasing birth weight.
The majority of fetal growth occurs 3 months prior to calving. Therefore, the temperature departure of the last three months is useful in judging if increased calf birth weights should be expected. October was pretty much normal. November was 3 degrees colder than normal, December was nearly 5 degrees colder than normal and January is 6.3 degrees below average. For perspective January 2014 ranks as the 17th coldest on record, but 1977 was 16 degrees below normal. Yikes! Can you imagine your Dad trying to calve those giraffe-legged cattle in the winter of 1977...bet it wasn't pretty.
So in summary, not much research has been conducted to answer this question. Other factors like sire selection, pelvic area, overfeeding, and body condition score likely have more of an impact on calving success. Colder temperatures will likely lead to an increase in birth weights... however the difference due to temperature will likely be subtle.