Growing trees on a terrace is much more difficult than growing them in a garden. The main problems to be contended with are intense sun and high winds. Practical considerations such as the size of the root ball associated with a mature tree, the amount of soil that a terrace can hold and the availability of water are also important.

For these reasons it is preferable to select dwarf varieties of trees unless adequate space is available and weight considerations are not important. Also, pay particular attention to the hardiness of the suggested  trees. Trees that may be suitable for a street level garden may not be hardy in an exposed location. Depending upon the extent of the exposure of your terrace, you should select plants that are hardy one or two USDA zones lower than yours.

Here is a list of some possible trees:

Conifers

Eastern white pine. Pinus strobus. Hardy to USDA Zones 2 - 3. 'Coney Island' is a dwarf varietyL

Mugo pine. P. mugo. To Zone 2. 'Paul's Dwarf' is a miniature variety.

Limber pine. P. flexilis. To Zone 4. 'Vanderwolf's Pyramid' and 'Bergman's Dwarf' are dwarf varieties.

Hinoki cypress. Chamaecyparis obtusa. To Zone 5. 'Nana Lutea' is a dwarf variety.

Eastern hemlock. Tsuga canadensis. To Zone 3. 'Jervis' is a dwarf variety.

Eastern red cedar or flaky juniper. Juniperus virginiana 'Blue Mountain' and Juniperus squamata 'Blue Star' are dwarf varieties. To Zone 4.

Other trees and shrubs

River birch. Betula nigra. To Zone 4. 'Little King' is a dwarf variety.

American dogwood. Cornus florida.  To Zone 5.  Suitable for a large terrace. Dwarf varieties are also available, e.g. 'Little Princess' and ' Suwanee Squat'.

Kousa dogwood. C. kousa. To Zone 5. Suitable for a large terrace. Dwarf variates are also available, e.g. 'Little Poncho'.

Japanese maple. Acer palmatum. To Zone 5. Suitable for large terrace. Dwarf varieties are also available, e.g. 'Red Dragon'.

Serviceberry. Amelanchier spp. To Zone 3. Suitable for large terrace. Dwarf varieties are also available, e.g. 'Regent'.

Harry Lauder's Walking Stick. Corylus avellana 'Contorta'. To Zone 4.

Smoke Bush Cotinus coggygria. To Zone 5. Suitable for a large terrace. For smaller terraces it can be pruned back drastically each spring (although it will not then flower)..

Mountain laurel. Kalmia latifolia 'Elf". Hardy to Zone 5.

Climbing hydrangea. Hydrangea anomala subsp. petiolaris. To Zone 4.

You can find more information on planting for a terrace in the NYBG guides Urban Gardening and Conifers as Container Plants.

Courtesy of NYBG Plant Information Service