That is relatively safe, providing that you use SSL (HTTPS, use ssllabs to check the security of your site), and you configure your cookie to be domain-specific, have an expiry date not too far in future and be "HTTP-only".
Use mcrypt for encryption (there's support for that in PHP) and the salt key should be reasonably long, and kept SECRET, or change for each cookie (this is a little more complicated).
Also, consider what is the sensitivity of the information you hold for the user, and assess what would be the worst consequences if someone has stolen your user's data.
By definition, a system is secure if the cost of hacking it is greater than the intrinsic value of the data that can be stolen. Use this rule as a discriminator for your security assessment, to determine if you should worry about some more advanced techniques, of if the ones listed above would be enough.
It is also worth mentioning that - if the mentioned above was not enough, you should probably NOT offer your users the "remember me" option: banks do not do that, for obvious reasons.