BASH How to use each line of a file as a variable input within for loop

A cautious answer might look like:

readarray -t users <users.txt
printf -v cmd_q '/home/%q/newdir ' "${users[@]}"

for (( counter=0; counter<99; counter++ )); do
  printf -v counter_padded '%02d' "$counter"
  ssh "user@server${counter_padded}.domain.com" 'bash -s' <<<"mkdir -p -- $cmd_q"
done

What noteworthy advantages (and disadvantages) does this have?

• We require bash 4.0 on the local system, for the readarray feature. This lets us read users.txt only once, populating an array "${users[@]}", which we then use to generate a string "$cmd_q", which a shell-quoted version of our list of home directory names (more on that later!)
• Using the %q format string is guaranteed to generate an eval-safe shell-quoted string (when the remote shell is provided by bash), so some joker saying their username is $(rm -rf ~) won't cause you a bad day.
• There's no dependency on a nonstandard seq, command, and no letting ssh combine its arguments to generate a string to pass to the remote command -- instead, we pass it an explicit list of arguments, already correctly quoted.
• We run mkdir only once, not a separate time per directory name. (xargs is capable of doing this kind of thing too, but it turns off that behavior when used with -I{}).
• $(...anything...) is generally slow, and we avoid it here. That won't result in a noticeable performance difference in this particular case (since another approach wouldn't necessarily put the command substitution in the loop body at all, and even if it did, ssh is much slower by comparison), but it's a good habit to get into for when you have a use case where your loop could otherwise be fast.

If you needed this to run with an arbitrarily large list of usernames, I would change mkdir -p -- $cmd_q to printf '%s\0' $cmd_q | xargs -0 mkdir -p --, which can handle more filenames than can fit on a single mkdir command line. (Because printf is a shell builtin, not an external command, it isn't subject to the operating system's command-line length limits).

You just need an inner loop. Here's one way which uses xargs on the remote server, passing the usernames through on stdin. (Also illustrated: using printf to generate the list of server names. But note that this requires that the server name not include whitespace or any other shell metacharacter)

for server in $(printf "user@server%02d.domain.com" $(seq 99)); do
  cat users.txt |
  ssh -o StrictHostKeyChecking=no $server \
      xargs -I{} mkdir "/home/{}/newdir"
done

That works because the command you're running on the remote server is a single shell command, but it's not totally obvious how to extend that to a more complicated command. It's also not the most efficient since you could have created the three (or however many) directories with a single mkdir.

If the script you're trying to run on the remote server is not too complicated, you can wrap it in sh -c or even bash -c (if bash is installed on the remote hosts and you want to take advantage of its features). This works for simple sequences of commands, but managing quotes properly when you have two levels of quotation going on can be a real headache.