Here are some plants that thrive well in each zone, according to the U.S. Department of Agriculture:

Zone 1
Average annual minimum temperature below -50 degrees

Betula glandulosa (dwarf birch)
Empetrum nigrum (black crowberry)
Populus tremuloides (quaking aspen)
Potentilla pensylvanica (Pennsylvania cinquefoil)
Rhododendron lapponicum (Lapland rhododendron)
Salix reticulata (netleaf willow)

Zone 2
Average annual minimum temperature -50 to -40 degrees

Betula papyrifera (paper birch)
Cornus canadensis (bunchberry)
Elaeagnus commutata (silverberry)
Larix laricina (eastern larch)
Dasiphora fruticosa (shrubby cinquefoil)
Viburnum opulus var. americanum (American cranberry-bush)

Zone 3
Average annual minimum temperature -40 to -30 degrees

Acer saccharum (sugar maple)
Elaeagnus angustifolia (Russian olive)
Hydrangea paniculata (panicle hydrangea)
Juniperus communis (common juniper)
Lonicera tatarica (Tatarian honeysuckle)
Malus baccata (Siberian crabapple)
Parthenocissus quinquefolia (Virginia creeper)
Spiraea x vanhouttei (Van Houtte spirea)
Thuja occidentalis (American arborvitae)

Zone 4
Average annual minimum temperature -30 to -20 degrees

Berberis thunbergii (Japanese barberry)
Juniperus chinensis (Chinese juniper)
Ligustrum obtusifolium subsp. suave (Amur privet)
Ligustrum vulgare (common privet)
Parthenocissus tricuspidata (Boston ivy)
Taxus cuspidata (Japanese yew)

Zone 5
Average annual minimum temperature -20 to -10 degrees

Acer palmatum (Japanese maple)
Cornus florida (flowering dogwood)
Cotoneaster microphyllus (small-leaf cotoneaster)
Deutzia gracilis (slender deutzia)
Euonymus fortunei (winter-creeper)
Rosa multiflora (multiflora rose)

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Plants for growing in zones 6-10