Ptarmigans are rather easy to find in Iceland when you are not hunting them. The ptarmigan (lagopus muta) is very common and is the only grouse we have in Iceland. In the summer-months it´s possible to find it almost everywhere. In the winter it mostly stays in mountains and rocky landscape depending on the weather. The absolutely most easy way to photograph them is in Hrisey, which is a small island in north-iceland. There they are not nearly as shy as those in the mainland.
It´s a good idea to search for ptarmigans in heath or grassland areas during summer and since they prefer cold and dry weather conditions they can be found in mountains in winter. All lenses can be used for ptarmigan photography. Long telephoto lenses are best, but I have even used the Nikon 14-24 f2.8.
If you take your time it´s possible to get within two meters from ptarmigans. It takes time. By stopping once in a while and waiting for them to calm down it´s possible to use the widest of lenses like my wife, Gyda Henningsdottir is doing in this photo taken in Hrisey. She is using Nikon D3 with the 14-24 f/2.8 lens. None of the best lenses for bird photography replace the benefits of getting real close to the subject. This is why I always keep a pouch ready for my teleconverter when using one for the longer lenses. Very often the subject ends up by getting too close for the framing or even for the closest focus distance. That´s when it handy to be able to take the converter off since you are getting really close.