If you have every melted snow in the woods, you know that when you are done there are quite a few chunks floating around in the pot. You can try to flick them out with your spoon. You can try to ignore them in your oatmeal, or you can use a strainer.
In the past we have used an MSR mug-mate. It works great, but it just barely fits into the opening of a nalgene. I intend on taking a small thermos, so that I can have a hot drink or soup for lunch. So, my quest was for a smaller version. Of course my wife came through and got me a single cup attachment for the Keurig coffee maker for x-mas.
The second problem you have in the winter is that if you get a small chunk of ice in the threads of the nalgene, you will get a leak. With most of us using these to heat-up our feet in our sleeping bags - this could spell trouble' I.e.; wet feet in the morning.
A Keurig/Nalgene lid was born. It protects while it strains.
Disclaimer - while this will help with dirty snow, it will not help with yellow snow.