Arm to arm co-ordination is a natural rhythmical effect but aggressive over use of both can lead to performance loss. We need to drive our arms to help our legs up a hill but on the down our arms should be relaxed and our legs flowing without over striding. On the flat we are looking for a mid way type cruise.
Newcomers running up a hill tend to fade to a walk before the top and when a level or down arrives find themselves struggling to get going again.
To try and overcome this, whilst we need to drive the arms, a shortening of the stride can help to lessen leg muscle fatigue. In other words do not kill the hill. Once at the top you should be able to get back flowing, not forgetting to relax on the down.
Another tip for running up hills is to look down at the ground with only the occasional look up, as to focus too much looking for the top can be a recipe for mental fatigue. In other words let the hill come to you.
Whilst this information is primarily for training, slight adjustments can be made to suit ones own speed when at races.
All in all try not to panic and try to run with a relaxed momentum and mindset.