What is a suitable Tensorflow model to classify images into foggy/not foggy? I want to classify photos taken by multiple webcams that are operating in mountainous regions into foggy / not foggy. The photos are in various sizes and were taken under very different light conditions and in different areas.

I read about Tensorflow and its ready-to-use image recognition models (which of course would have to be re-trained for the foggy/non-foggy categories). 

However, these models are trained to classify images into categories according to objects within these images. As I want to classify my images based on their overall appearance (blurry, greyish, far away objects hardly detectable, ...) I was wondering if these models are really suitable or if there is a better approach for this task. Any help is highly appreciated!
From the sounds of the problem you could probably do some thing with extracting some features from the images such as how many edges they have, brightness (to get day/night), average color values. Then using a more simpler classification algorithm such as SVM, KNN, Decision Tree, Random Forest.

The Tensorflow ready-to-use models look to be very complicated models with a large number of layers so it will take a long time to train and run. It will also be very hard to train them from scratch (Retraining a pretrainid network could help with that though). So I think they might be a bit overkill. Also note that those models were probably made with the imageNet dataset in mind which has 1000 classes where you have just 2.

Its very hard to know what will work without seeing the images or being able to trying it first.

I would start with simpler faster methods before trying slower more complicated methods.
So in order try the feature extraction plus classifier if that is unable to learn a good relationship then move on to a basic CNN if that doesnt work move on to the more complicated CNN models.

With respect to the objects within rather than the overall appearance. For a CNN using different pooling layers can effect this change this. eg. Max Pooling will get the max value of a filter so can be largely effected by a small part of the image where as Average Pooling will be better at looking at the whole image.