Exclude .LOG file while restoring a database
No: the log is an essential part of the database and is used during RESTORE process (redo/undo phases) to ensure consistency.

Use WITH MOVE to restore to a compressed folder to gain "more" disk space temporarily. Or an external USB drive etc

Edit:

By compressed, I mean NTFS compression (for XP but still applies).

WITH MOVE is part of restore exposed as "Restore the database files as" in SSMS

Edit 2:

SQL Server can not use network drives unless you enable trace flag 1807. Now, use at your own risk to get running again only