OMG, we need to talk about northern China. And its FOOD.
But for now... yeah, the weather in winter in Beijing rivals the worst anywhere. Especially when you factor in the pollution. I think that is another reason the eyes water.
And summer in Beijing? Oy oy oy.
But at least the pollution isn't quite as bad in summer as it is in winter.
(Note, I'm not really an expert -- I haven't lived there, but have visited in different seasons. Might be back there again next year for a while. We will talk.).
So. Yeah.
I'm in a more temperate place right now. But back in Ontario my strategy was to bring a little sack of make up basics with me. I don't wear foundation but do wear concealer, mascara, eye pencil, eyebrow pencil, lipstick. There is no "final destination" but there will be some kind of bathroom somewhere (most of the time, at least) and so like LisaP, I will do intermittent touch ups where required. Waterproof mascara, liner, brow stuff help the eye area and minimize the need to deal with that. I typically touch up concealer and lipstick and/or lip balm much more often.
For the dryness -- I use a super emollient nighttime moisturizer. Like, crazy emollient. (I'm older than you so my skin is dry anyway. In dry weather it just soaks up the moisture like a paper towel.)
I also drink a ton of water, which I know can be an issue in China where you are confined to boiled or bottled and then you have to think about all that plastic...