On one hand, troops that are not close enough to a detonation to avoid instant death or LD50 or greater radiation exposure are better equipped than civilians to survive. They have training, even units without NBC trained specialists with them have some training and probably some radiation detection equipment. They know how to decontaminate, what to avoid. To some extent they have some supplies, and they are armed and trained in the use of weapons. If a unit has NBC folks with them, if they have even a small medical detachment so much the better. This is short term, long term they are better off but as supplies run short they have the same issues about food and water as everyone else. There will be a particular issue for troops which are not local or close to it. A large number of the troops may not speak the language of where they are when the nukes light off. For US, Canadian, and British troops in Europe there is water between them and home - in theory both WP and NATO troops can walk home. The further away from home the greater the stress on any troops. If your home is in Bonn, for example, and Bonn has been nuked, you will accept your family is dead. If you are from Little Rock, Arkansas and when the world explodes you are in Norway with the Marines, every day is going to start and end with "where is my family, are they alive or dead, they need be to be there with them". That will eat at you - a certainty your family has perished (hopefully instantly) is bad, a constant uncertainty and fear about their status is much much worse. Suicides will be a major issue, especially with troops who can't try and go home.
Longer term a lot will depend on where a unit ends up, and how large the unit is and what assets they have. There are several possibilities. A unit can become a warlord band. They can settle down with locals with protection as part of the community and potentially a seed for some recovery. A unit can break apart and individuals assimilate in to the local population losing any identity.
Obviously troops in or around obvious nuclear targets will be devastated, I expect things like armor units in the field will be targets. Essentially troops in the field away from military or civilian targets have the best chance of riding out the mushroom clouds.