Couple of question - what is the incline on your treadmill? If you have one are you more comfortable running on a lower incline?
Also, how fast are you trying to run? I agree with the slow down part. You don't have anything to hold onto when running outside (and trust me I've fallen running outside) and you automatically adjust your pace which the treadmill doesn't allow you to do.
Fundamentally, I'm very uncomfortable running and holding onto the bar but it is because of the pacing reasons.
It's up to you on how you run - but I would maintain one natural running stride whether you are on a treadmill or not. If you swing your arms, you can't do that holding onto the bar of a treadmill and that changes your stride and may stress your body is some different ways.
Lots of food for thought but fundamentally - be safe. That's most important.
SEP12: Rock N Roll HM: 3:04:04
| current weight: 150.2