Don't try to fine-tune your exact schedule for the optimal weather in each place. Northern Manchuria extends as far north as parts of Southest Alaska. Beijing is at the latitude of Philadelphia, Hong Kong as far south as Havana. East China gets enough rain year-round for paddy rice. Much of central China is semi-arid steppe.
Similar issues arise in other regions.
We hit New Zealand in mid-winter and it was spectacular. And a great contrast to the previous two months on South Pacific islands in the sun. It isn't natural and doesn't give you a true picture. Sure, be aware that there are times when trekking is difficult to impossible, and that roads may get washed away, or closed due to snow. In our case we ended up in the Southern Hemisphere in Winter, and a lot of people told us to avoid it.