As an update to this thread, looks like the new function is floatmin:
help?> floatmin
search: floatmin floatmax float flatten Float16 Float32 Float64 findmin Cfloat
floatmin(T = Float64)
Return the smallest positive normal number representable by the floating-point
type T.
On a x86_64:
julia> floatmin(Float32)
1.1754944f-38
julia> floatmin(Float64)
2.2250738585072014e-308