I never tie down the front and we've pulled the bikes several times on 1000 miles each way trips:

 

^ Scott, do as you wish but I *highly* advise securing the front end in some fashion. Just b/c you've not had any probs or incidents, doesn't mean you won't. Taking a few min to secure the front end is just a good practice to prevent any unforeseen probs.

Btw, nice wheels on your trailer. ;-)

 

If you're not doing a tie-down on the front via suspension/bars...
I'd, at least, recommend binding that front wheel in the carrier.
A really bad bump or an evasive manuveur with the tow-vehicle,
while rare, aren't improbable.

Ern