Try following awk
awk 'NR==1 {next} NR==FNR { for(i=1;i<=NF;i++) sum[i]+=$i; next } { for(i=1;i<=NF;i++) if (sum[i]==0) printf " %s", $i; print "" }' file{,}
Output
C1 C3 C5
0 0 0
0 0 0
0 0 0
0 0 0
Idea here is to iterated of file twice. Once it calculates sum of all columns and in next iteration it prints only columns having sum equal to zero.
This assumes all column entries have positive numbers only
Another, may be better, approach would be to set a flag if any entry in a column is non-zero. And then print only those columns for which correspondig flag is zero.
awk 'NR==1 {next} NR==FNR { for(i=1;i<=NF;i++) if ($i) flag[i]=1; next } { for(i=1;i<=NF;i++) if (!flag[i]) printf " %s", $i; print "" }' file{,}
This approach allows positive as well as negative numbers and removes any restriction.
Or as suggested by @fedorqui in a comment
awk 'NR==1 {next} NR==FNR { for(i=1;i<=NF;i++) if ($i) flag[i]=1; next } { for(i=1;i<=NF;i++) if (flag[i]) $i="" } 1' file{,}