Your logic is not too far off. One way to deal with your issue with minor changes to code would be to add a layer of depth to hash of arrays:

#!/usr/bin/perl -w
use strict;
use List::Util qw(max);
use List::Util qw(min);

#my $input0 = $ARGV[0];
#open (DATA,$input0) || die "cannot open input0";

my %gene_hash;
while(<DATA>)
{
    chomp;
    my ($chr, $start, $end, $gene, $ex) = split(/\t/, $_);
    my $gene_key = $chr.":".$gene;
    
    push( @{ $gene_hash{$gene_key}{start} }, $start ); 
    
    push( @{ $gene_hash{$gene_key}{end} }, $end ); 
   
    push( @{ $gene_hash{$gene_key}{ex} }, $ex ); 

}



foreach my $key (keys %gene_hash)
{
    my ($c, $g) = split(/\:/, $key ); 
    print "$c\t$g\t";


   my $Low=min( @ {$gene_hash{$key}{start} } );   
  
   my $High=max( @ {$gene_hash{$key}{end} } );
  
   my $High_ex=max( @ {$gene_hash{$key}{ex} } );

   

    
    {
    
        print "$Low\t$High\t$High_ex";
    }
    
    print "\n";
}

__DATA__
chrX    2680092    2744539    XG    1
chrX    2680090    2744529    XG    2
chrX    2680080    2744519    XG    3
chrX    2680070    2744509    XG    4
chrX    2680070    2744509    DT    1
chrX    2680090    2744519    DT    2
[download]

If the modification is unclear, you can use Data::Dumper to output the resultant structure by adding the following to the end of your script:

use Data::Dumper;
print Dumper \%gene_hash;
[download]

A couple of minor things you may consider in addition:

1. You should probably get into the habit of using 3-argument open instead of 2-argument open; the difference is explained in perlopentut.
2. You might also consider swapping to Indirect Filehandles. This can become important in larger projects.
3. split acts on $_ if no argument is given, so you could change that call on line 13 to = split(/\t/);
4. You delimit your keys with ':'; if you are going to create an amalgam key, you should use a character that is guaranteed not to appear in your file - might I suggest "\t"? That way you don't have to split it again for output.