Hi, You can remove the cones in spring just before the new growth begins. Keep the cones just in case the weather takes a cold turn.
Roses should be trimmed in very late winter or very early spring before the leaves begin to bud. If you mean rose hips, they can be trimmed any time. In our location most the rose hips are eaten by the wildlife before the winter is over, but you can remove them now if your roses still need it.
I remove the "dead heads" (left after buds bloom n withers) any time. As with all my flowing plants, removing the "dead heads" promotes additional growth of buds not to mention keeping them from being eye sores.