My daughter has had disturbed sleep since she was born, (thankfully beginning to improve now), and resultantly I have had 5 years of disturbed sleep.
This certainly impacts on recovery, as mentioned above. The biggest impact I find poor sleep has on physical health is that it erodes willpower. When shattered I just can't muster the energy to attempt hardstyle swings, get-ups or prying squats.
The greatest thing I've taken from these forums thus far is to have an exercise one can attempt even on our weakest day. Thanks to a post by Steve I now use the Cook Carry routine. Although I don't do it to failure as Gray advocates in the video, and often I haven't space to walk so I stand on one leg, which still fires the stabilising muscles. This approach allows me to keep consistent with my training.