Here is a concise example based on @Tamas_Papp 's suggestions.
nanmean(x) = mean(filter(!isnan,x))
nanmean(x,y) = mapslices(nanmean,x,y)
julia> y = [NaN 2 3 4;5 6 NaN 8;9 10 11 12]
3×4 Array{Float64,2}:
NaN 2.0 3.0 4.0
5.0 6.0 NaN 8.0
9.0 10.0 11.0 12.0
julia> nanmean(y)
7.0
julia> nanmean(y,1)
1×4 Array{Float64,2}:
7.0 6.0 7.0 8.0