When using System.Net.WebRequest your application will negotiate with the server to determine the highest TLS version that both your application and the server support, and use this. You can see more details on how this works here:
http://en.wikipedia.org/wiki/Transport_Layer_Security#TLS_handshake
If the server doesn't support TLS it will fallback to SSL, therefore it could potentially fallback to SSL3. You can see all of the versions that .NET 4.5 supports here:
http://msdn.microsoft.com/en-us/library/system.security.authentication.sslprotocols(v=vs.110).aspx
In order to prevent your application being vulnerable to POODLE, you can disable SSL3 on the machine that your application is running on by following this explanation: