Keep in mind that the focal length is for a full frame sensor on a crop sensor you'll have to multiply the crop factor for a similar focal length, especially on the wider end.
I would recommend a longer lens 200-500mm would be preferable for photographing the deer if you want close ups or a more normal lens between 50-100mm if you want to capture a more environmental picture of the deer.
When capturing the nature scenes I would recommend wider lenses 14-50mm would be my recommendation. Since you can get so close to the everything with ease and the trees are so big I would say that it would actually be harder to use a telephoto lens even when you want to capture detail. But if you really prefer detail shots over environmental shots then I think that a 70-200mm would be great.
I had three lenses with me during my visit, a 16-35mm f/4 VR Nikkor, 50mm f/1.8 Nikkor, 70-200mm f/2.8 OS Sigma. 200mm wasn't really enough for capturing the deer inside the forest, where they appear to be more shy. I would have loved to have had a 200-500mm f/5.6 VR Nikkor with me instead of the 70-200mm. When I was walking around and photographing the nature then I was very satisfied with the 16-35mm. The flexibility of wider angles really works well in this park since the trees are so big.
If you ever have the opportunity I would definitely recommend that you take a walk in the park, you can go through the whole park in under 30 minutes so it really isn't that big of an undertaking. It's an experience that I'm confident that you will not regret. The park offers a old kind of nature that is almost non existent in the wild anymore. The only places that I have seen that have the same kind of nature are other natural reserves where that kind of nature is enforced. Hjorthagen is a prime example of this unique old type of forest and receives a huge recommendation form me.