Rhine doesn't freeze over in 406 AD

The winter of 406 was very cold, cold enough for the Rhine to freeze solid and allow hordes of barbarians to cross freely. What would have happened if the Rhine hadn't frozen over and the number of barbarians entering been reduced? Could the Western Empire have survived longer?
 
The winter of 406 was very cold, cold enough for the Rhine to freeze solid and allow hordes of barbarians to cross freely. What would have happened if the Rhine hadn't frozen over and the number of barbarians entering been reduced? Could the Western Empire have survived longer?

A little longer maybe, but probably not much.

At some point the Visigoths will enter Gaul (perhaps in Roman employ against Constantine III) and once Gaul is lost the WRE is on borrowed time. It may last a bit longer if nobody crosses to North Africa, but that's a big if.
 
Plus I believe the climate was generally getting colder at the time due to the end of the Roman Warm Period, so the Rhine could've easily frozen over anytime in that era.
 
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