I often talk with people and they are not quite sure when is the best time to go on a tour. There are so many questions that need answering that it’s quite impossible to give a clear and definite answer. The only answer I can give is that you should go on a bike tour as soon as you are ready and able to do it.
For some people, it might be a long-game, where they plan years ahead, waiting for retirement, for the kids to be old enough to join them, or just to save the necessary funds. Others may want to wait a year or more to save some money, buy top quality equipment so as to provide a level of comfort and assurance that in the worst scenarios, they know they can rely on their equipment. Others yet may not even wait that long, but just go on a whim because they have a bike and enough gear to survive for the duration of whatever trip they are on.
I personally tend to fall into the last group, having never planned more than a month or so in advance before going on a cycling adventure.
For the most part, the season, temperature, terrain, and weather in which you are travelling is only relevant to the bike tour when considering the gear you would need to take and the amount of preparation needed ahead of time. People have bike toured across the centre of Australia and across the Arctic regions of Canada, the USA, and Russia, braving temperatures in excess of 50°C and below -40°C
Needless to say, if you do decide to bike tour in more extreme conditions, you may need to spend more time preparing before you can start.