Usually with vagrant ssh <box> a connection to the box can be made via ssh.
When putty is preferred as ssh client then this is possible, a vagrant plugin (vagrant-multi-putty) is available for this.
just goto the command line and issue this command: vagrant plugin install vagrant-multi-putty
Be sure that the putty binary can be found, if not the put the location of the putty binary in your path.
Example on Windows:
Login into a single vm in a multiple vm environment:
vagrant putty <name of vm>
Pass putty options directly to the putty binary:
vagrant putty — -l testuser -i <path to private key>