The modeled settling speed of frozen hydrometeors has important implications for the prediction of weather and climate. However, it is usually assumed, erroneously, that they fall in still air. Here, we present novel field measurements of individual snowflake microphysical properties and their settling velocities in atmospheric surface-layer turbulence. Individual snowflake motions are tracked in a laser light sheet using particle streak velocimetry (PSV). A hotplate device, the Differential Emissivity Imaging Disdrometer (DEID), is used to obtain precise estimates of snowflake mass, density, and size. Relative to calculated terminal velocities in still air, we present enhancements and reductions of snowflake settling speeds in turbulent air for a broad range of Reynolds and Stokes numbers. Functional forms describing actual snowflake fall speeds are presented and explored. In particular, a promising non-dimensional functional form for the ratio of actual particle fall speed to terminal velocity is presented in terms of turbulence intensity and a new variable called the shape density index or SDI, which is related to an individual hydrometeor's microphysical structure.