My skin always gets so dry in winter, and I often have to skip foundation as it sits horribly on my face when It's dry. However over the years I have found some products that help combat that! Adding an extra moisture layer in my skincare routine is always important in winter, I've been loving the Pixi Hydrating Milky Lotion. I then follow this with a thick moisturiser or oil. At the moment I've been opting for an oil and am using The Ordinary Moroccan Argan Oil, only using a few drops.
When my skin is desperate need of hydration I use the Weleda Skin Food, introduced to me by a friend at Uni. I was so put off this at the start as it's pretty sticky and very thick but applied over a milky serum it works so well to re-hydrate my skin. I use it a lot at night all over my face.
To combat the 'dry nose' look, a trick I discovered years ago is to use an eyeshadow primer over the super dry areas on your face that foundation tends to stick to. MAC eyeshadow bases work really well.
My fail safe foundation that I recommend to everyone is the IT Cosmetics CC+ Cream. Oh my goodness, this product just never lets me down. It's a real hybrid of skincare and makeup, with factor 50!! So no need to add an extra facial SPF in the morning. I use the shade fair. If you're looking for a concealer that will probably last you a good 20 years (not that you should keep makeup that long haha), their Bye Bye Under Eye concealer is great. You need the tiniest amount and it covers dark circles really well, which in winter I really need.