How can I execute a set of .SQL files from within SSMS?

While SQLCMD.exe is the best way, SSMS also has a SQLCMD mode where you can execute a SQLCMD script. To enable this mode click Query in menu bar then select SQLCMD Mode.

The ":r filename.sql" command is the SQLCMD script command to import and execute a sql script file. You know you are in SQLCMD mode because any lines that are SQLCMD script commands will appear with colored (gray I think) background.

:setvar path "c:\Path_to_scripts\"
:r $(path)\file1.sql
:r $(path)\file2.sql

Use SqlCmd.exe.

For example:

sqlcmd -S myServer\instanceName -i C:\myScript.sql

or to save output to a file:

sqlcmd -S myServer\instanceName -i C:\myScript.sql -o C:\EmpAdds.txt