While Pinus strobus is frequently labeled as a zone 3 plant I will caution from experience that all stobus winter burn badly in my zone 3a area. When protected from late winter sun and drying winds the cultivars can survive in 3a (this is possible because they stay small enough to protect for many years).
Gerd Krussmann states in 'Manual of Cultivated Conifers' ........... 'Dwarf, umbrella-shaped shrub, 2-2.5m high, much wider than high, dense, but usually not branched to the ground. (I will add that the single stem at the base leading to a widely branched top over time leads to the umbrella shape and thus the original name). Krussman goes on to state that ... needles are gray-green with gray-white undersides. Often incorrectly labeled as P. strobus 'Radiata'. In maturity the difference between Radiata and Umbraculifera is evident. Radiata does not develop the umbrella shape. Both cultivars are also improperly sold under the name P. strobus 'Nana'. Welch has written in "Manual of Dwarf Conifers that he considers Umbraculifera a dwarf form of P. wallichina.'
Adrian Bloom refers in his book 'Gardening With Conifers' that the cultivars 'Blue Shag', Nana and Radiata are somewhat of a similar type. He also points out the variability mentioned by Krussmann of improper naming of Nana and Radiata but he does not mention Umbraculifera even though I expect it pre-dates the other similar cultivars considerably.