Strength training is a controversial topic when we discuss optimizing of training programs for cyclists. There is no definitive answer to whether cyclists should include weight lifting in their winter training plans. There have been made several studies which have not yet proved that cyclists can benefit from strength training.
One of the biggest problems for these scientific studies is that they are done at untrained people and the study group is usually small. That makes it rather difficult to prove a significant difference between endurance training only versus endurance training combined with weight lifting.
My best guess is that strength training does make a difference and it is, at least in theory, possible to prove it with a larger study group. But the difference between including strength training or not, is obviously not the most important factor when it comes to overall performance in road races.
Thus, it is very difficult to recommend you to either go to the gym or spend an extra hour on the bike. In both cases you will probably improve your overall performance level. It is important to notice that even though studies about strength training does not produce significant gains in overall cycling performance, it is very likely that there is a difference.
As I wrote in a previous post about strength training, many cycling coaches do not have an idea of what they are doing in the weight lifting gym. It seems like they are trying to convert their training principles from the cycling world into the weight lifting world. I believe that cycling coaches should listen to people who are more experienced with developing explosive power.
Track and field coaches have a very scientific approach to strength training. Olympic style weight lifters are experts at improving power without gaining additional body weight. Knowledge about strength training increases in a very accelerated pace, but nevertheless, most riders stick to their conservative training principles. I hope that more riders and coaches will open up their eyes and discover what is going on.