Cannot find Database Mail feature in SQL Server Express 2012 SP1
You can use SQL Mail with SQL Server Express edition.  

Borrowing liberally from Sending Mail using SQL Server Express Edition

To configure SQL mail we need to follow below steps.

--Create Sysmail Account
--Use sysmail_add_account_sp stored procedure of MSDB database to configure sysmail  account.
EXECUTE msdb.dbo.sysmail_add_account_sp
@account_name = 'MailTest',
@description = 'Sent Mail using MSDB',
@email_address = 'YourEmail@test.com',
@display_name = 'DisplayName',
--@username='umashankar@queryingsql.com',
--@password='password',
@mailserver_name = 'mail.server.com'

--Creating Database Profile
--Use sysmail_add_profile_sp stored procedure of MSDB database to configure Database Profile.
EXECUTE msdb.dbo.sysmail_add_profile_sp
@profile_name = 'MailTest',
@description = 'Profile used to send mail'

--Add database Mail account to profile
--Use sysmail_add_profileaccount_sp stored procedure of MSDB database to map database mail account to Profile.
EXECUTE msdb.dbo.sysmail_add_profileaccount_sp
@profile_name = 'MailTest',
@account_name = 'MailTest',
@sequence_number = 1

--Grants permission for a database user or role to use a Database Mail profile.
--To Grant permission for a database user or role to use a Database Mail profile use sysmail_add_principalprofile_sp.
EXECUTE msdb.dbo.sysmail_add_principalprofile_sp
@profile_name = 'MailTest',
@principal_name = 'public',
@is_default = 1 ;

--Enable 'Database Mail XPs'.
sp_configure 'show advanced options', 1;
GO
RECONFIGURE;
GO
sp_configure 'Database Mail XPs', 1;
GO
RECONFIGURE
GO

--Send Mail using Created Profile
exec msdb.dbo.sp_send_dbmail @profile_name = 'MailTest', @recipients = 'receiver@queryingsql.com', @subject = 'Mail Test', @body = 'Mail Sent Successfully', @body_format = 'text'




I will say that SQL Mail is deprecated and may be removed in a future version of SQL Server Express, but it still seems to work in the latest edition.