Based on @Jim Lewis's approach:
Here is a quick solution using find
and also sorting files by their modification date:
$ find directory/ -maxdepth 1 -type f -print0 | \
xargs -r0 stat -c "%y %n" | \
sort | cut -d' ' -f4- | \
xargs -d "\n" -I{} cmd -op1 {}
For sorting see:
http://www.commandlinefu.com/commands/view/5720/find-files-and-list-them-sorted-by-modification-time