The SQL CE instance is for the Web Access interface, which is optional. You can write syslogs to log files and the only limitation is on disk space.
Do you need all the logs over the year to be searchable or just archived? All searchable would probably require a full SQL server or other searchable storage. Just archiving to disk would only require enough space.
Determining how big the drive would need to be is going to be based on volume. A typical syslog is 1k or less so you can multiply your hourly rate by that. Then multpily that by the hours in a year. This would be a rough estimate since message rates and sizes vary. Also, since this is text it is highly compressible, either by the filesystem or with 7zip or similar.