Answer: That's a tough location with so little sun. Most flowering vines are tropical in origin, prefer more sun, and will have trouble surviving your winters. Here are some possibilities that can tolerate some shade and are rated to withstand the winter.
Campsis radicans or common trumpet creeper/trumpet vine is deciduous, will die to the ground in a hard freeze, but comes back. Flowers are in the yellow-orange-red range. Trumpet vines are usually very easy to grow.
Consider clematis. There are dozens of varieties and most are deciduous. Flowers are exotic looking and come in many colors. Roots need to be kept cool, and tops of the vines in the sun for growth and flowering. Clematis alpina, C. jackmanii, and C. recta are several rated for cold.
Aristolochia durior (also sold as A. macrophylla) or Dutchman's pipe. Deciduous (will lose leaves in fall). Covers 15 x 20 in one growing season. Large, kidney shaped leaves are deep glossy green. Blooms late spring to early summer. Unsual flower is yellowish green, curved tube shape that flares into brownish purple lobes. Takes full sun to heavy shade, needs plenty of water.
Most honeysuckle varieties aren't rated for cold winters, but you could consider Lonicera brownii, which is deciduous, grows to 9-10 feet, with scarlet tubular flowers that can bloom from early summer to frost. Takes full sun or light shade and moderate water. There are many honeysuckle varieties, so check with a local nursery for others.
Sweet peas are delightful, but they need sun to get started, and don't last when the weather gets too warm, although in a shady location they'd last longer.
Another possibility is a hardy climbing rose, assuming that thorns are not a problem in that location.
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