A simple solution using the same approach, is to convert the 0s to NaN, so as to ignore them in scatter():
U = rand(Binomial(1,.3) , T);
U2_ = convert.(Float64, U);
U2_ = reshape(U2_, 100, m);
U2_[U2_ .== 0] .= NaN;
scatter!(t_, U2_, c=:red, ms=4)