In reply to Robin Woodward:
In general the risk from being injured and tied in is often lower than the risk from not being tied in. I would generally do this if there are good rock anchors and the conditions are somewhat dubious (but should be okish) and the fallout zone is bad (ie there is a terrain trap beneath me, perhaps a narrowing where I could get buried or a cliff edge I could go over or rocks I could hit). You may find this worthwhile when crossing a gully, either when traversing along the cliff base or inside the gully when the edges seemed of reasonable risk to be unroped but the gully centre does not.
I've also done this approaching Good Friday Climb on the Ben as the final slope you traverse can be suspect and there are reasonable anchors and if the slope went you'd go an awful long way.
I would have to be more desperate to use this technique with snow anchors as I suspect they may not hold but it does depend if the risk is from a shallow surface avalanche or something deeper. I'm sure many people have been killed from only the surface layers failing when the deeper snow is solid.
Post edited at 16:56