This is a Jenkins user question rather than a Jenkins dev question. The Jenkins developer list is used for discussions of developing things for Jenkins, not for discussion of ways to use Jenkins to develop other things.
In your case, the answer is, yes, you can run a script on a Unix server from Jenkins on Windows.
You'll need a program that will allow you to run the 'ssh' command on Windows and have it run the 'sudo /sbin/shutdown -r now' command. Git for Windows provides ssh. Windows subsystem for Linux provides ssh. The chocolatey package manager for Windows includes a Win32 OpenSSH. Cygwin provides ssh. I'm sure there are others as well.
The user on the remote Linux system needs to be configured to allow the /sbin/shutdown script to be run from sudo. Refer to the 'sudo' man page and other online guides for sudo configuration instructions.
If those instructions are not sufficient to answer your question, please ask the question on the Jenkins users list. There are more people on that list than on this list and they are more likely to have dealt with this type of question.
Mark Waite