The question being answered here is, "Are things really bad enough that we're willing to brave all the kinds of dangers that the outside world has to offer?" This, obviously, depends on two things: How bad things are in the fortress, and how dangerous the outside world is. Good and/or benign regions, with their more inoffensive wildlife and such, would be more attractive for emmigrants to leave from, as opposed to he obvious dangers of evil and/or savage areas. Enemy invasions are also worth considering; if there's a lot of sieges or ambushes this time of year, and the group doesn't have a large military presence, it's improbable that they'd leave. (If they did, there should be a chance that any siegers/ambushers coming would encounter the emmigrants. This would likely lead to several siegers carrying gear from the fallen dwarves.)
Emmigrants will never leave during a siege. If the surroundng landscape is barren of easily edible plants or animals, the dwarves would be unlikely to leave. Finally, in some circumstances, the presence of a nearby sanctuary (i.e. another mountainhome, a friendly forest retreat, in desperate circumstances an abandoned town, etc) would lead dwarves to head there rather than striking it out in the wilderness. This would also relieve pressures against going for whatever reason--e.g, who cares that the wilderness doesn't have any food/we don't have any herbalists/our defenses would be inadequate? We're only going to be out of the sight of civilization for a day!