If you have newly planted trees, check their guys / stakes
before adverse winter weather strikes, which combined with wet
ground can cause trees to by windblown.
Your container shrubs and trees will still need watering during
winter, albeit at much lower levels. Likewise evergreen
trees use more water than deciduous trees in winter, as they retain
their foliage, if we have a dry winter they may require
watering.
Should we have snow, the weight of snow on branches can cause
them to bend and even break. Whilst it is still fluffly the
snow should be gently dislodged (whilst standing upwind). If the
snow has turned to ice it is better to leave it in situ.
As for protecting non native plants, the varieties from wamer
climates will have to be protected.
If there any any woodchips available, now is a good time to
place around specimens / top up existing, remembering to keep the
area around the trunk clear.