The large plants/trees in my garden have been damaged by the heavy snow over the past few weeks. We have a few of these plants and I'm not exactly sure what they are. The biggest is about 8ft tall with a single trunk. The smallest is a reddish leaf variety about 4ft tall. They occassionally grow another "trunk" from the base. I think they may be a cordyline.

The leaves which have always been very strong have fallen with the weight of the snow and now, although most of them still look rather healthy, they are just hanging down by the side. One of the plants has about 5 leaves still pointing straight up but it does look a bit silly.

Can anyone help. Not sure whether to cut them all off and hope that they start growing back or just trim the weakest from the bottom/underneath?