You mean that the winter after Hitler first invaded was paticularly bad? Yes, that's true. It's inaccurate to credit that to 'The Weather' though as there's never once been a year when Russia hasn't
had a bad winter, the only change was that this one was slightly worse.
It does speak about Germany's (or Hitler's, if you prefer) incompetence in planning this invasion. Hitler had planned to be in Moscow and have negotiated a Russian surrender by the time Winter came around. This not happening is often attributed to the German's having to help the Italians out in Yugoslavia and Greece, which was not planned. This resulted in Operation Barbarossa being delayed a few months and, consequently, less time before Winter (which is when the Russians finally managed to get up a feasible defence and counter attack).
Almost all German tanks were diesel fuelled engines at the time (as were most tanks anywhere). If you've ever tried starting a diesel engine car in winter imagine how much worse it would be in a chasis weighing several tons. Remember too, that this was back when Tanks were still radical, new and (most importantly) inefficient vehicles. The Russians often left their tanks running during winter.
Also, realise that because Hitler didn't expect the war to last into winter he did not equip his troops with Winter gear. The impact this had on the troops brought their efficiency far below that of the Russian winter divisions (some of which used horses when their trucks wouldn't start). Some believe Moscow would not have held out if it weren't for the Winter's affect on German troops. And the Russians did
manage to take large amounts of land around Moscow during the winter... Which the Germans never took back.