Should I shrink the Log File
Irrespective of Recovery model,shrinking wont help you if there is an active transaction or due to the  reasons mentioned here

Transaction log space will be reused in all recovery models irrespective of Size shown in file Explorer,you may still have free space..

Here is what MSDN has to say about Log space reuse..


  Log truncation frees space in the log file for reuse by the transaction log. Log truncation is essential to keep the log from filling. Log truncation deletes inactive virtual log files from the logical transaction log of a SQL Server database, freeing space in the logical log for reuse by the Physical transaction log. If a transaction log were never truncated, it would eventually fill all the disk space that is allocated to its physical log files.


How the log space will  be reused is different in different Recovery Models

1.In simple recovery Model,Log Truncation will happen after checkpoints which occur due to many factors as discussed here
2.In Full Recovery Model,TLOG space will  be reused only with Backups of Tlog

So even in simple recovery model,Your log space  has grown huge which means there is some thing which is preventing logspace reuse..so changing to Full Recovery Model also won't help unless you troubleshoot what is the cause..

You can use below query to see what is Preventing TLOG space reuse..

select log_reuse_wait_desc from sys.databases 


Further shrinking Log file is bad for many reasons some of them include
1.file growth operations are expensive
2.Instant file Initialisation wont help for log files    

Further Readings:
https://www.red-gate.com/library/sql-server-transaction-log-management