You could try the following. Say,
df <- matrix(sample(1:35,35),7,5)
> df
[,1] [,2] [,3] [,4] [,5]
[1,] 18 16 27 19 31
[2,] 24 1 7 12 5
[3,] 28 35 23 4 6
[4,] 33 3 25 26 15
[5,] 14 10 11 21 20
[6,] 9 2 32 17 13
[7,] 30 8 29 22 34
Say your threshold is 5:
apply(df,2,function(x){ x[x<5] <- max(x);which.min(x)})
[1] 6 7 2 2 2
Corresponding to the values:
[1] 9 8 7 12 5
This should give you the index of the smallest entry in each column greater than threshold according to the original column indexing.