smartphone and arduino relation

I am working on a project that would require an arduino to communicate with a smartphone to record data.
For this project I am looking to use an arduino nano to keep the overall size of the project small but if needed I also have an arduino uno. In this project I am looking for when turned on, the arduino can tell the smartphone to record data(ie: gps location, temperature, humidity, etc)through the use of bluetooth(an hc05 or hc06 module) and then send this data (either via text or email) to another smartphone or device that can accept a text message or email. Is it possible to have an arduino use a smartphone's built-in sensors?

Note: I have no experience using arduinos so I could really use some pointers to get me going in the right direction for this project.

Apart from Arduino issuing commands to Android, the first part of your proposal is thoroughly practical and indeed commonplace. I know nothing about the second part, it doesn't involve Arduino, and is probably neither. It is also probably not worth the effort, and indeed the wrong approach entirely.

Normal practice is that Arduino sends a data stream irrespective of whether the phone can receive it, and also records it locally. The same phone can also therefore download the recorded data at leisure. In both instances, the phone uses a standard terminal app.

You might find the following background notes useful.

http://homepages.ihug.com.au/~npyner/Arduino/GUIDE_2BT.pdf
http://homepages.ihug.com.au/~npyner/Arduino/BT_2_WAY.ino

A Nano would be fine but, if you are serious about miniaturisation, a Pro Mini would be better.