Yes, one or two ponies in a padded envelope will usually be under $3.
US shipping is determined by ounces and pounds as well as zip codes for heavier packages.
Anything under 13 oz. can be shipped First Class. The price changes every ounce after 3 oz. but it's the same no matter where it's going in the country. The lowest price is $2.07 and the 13 oz. price is $3.77. Insurance and tracking are extra (90 cents for tracking when purchased at the post office). You might be able to get up to 5 ponies to ship this way in an extra large padded enevelope (depends on generation and whether they're all adults).
Over 13 oz., you'll have to use Priority Mail (there's also Standard Post but I recommend staying far away from that as it can be extremely slow and doesn't save much money if any). This will depend on the zip codes as well as the weight. The price changes after every pound but also the further the package is going (the closest being about $5.60 for 1 pound and the furthest being closer to $7 for the same weight). Flat rate (have to use packaging provided by the post office) is almost always more than shipping normally (unless you're shipping bricks or something
). Priority now includes tracking and $50 worth of insurance as well.
Here's the USPS shipping calculator for you to play around with to get a better idea:
http://postcalc.usps.com/ You'll need to look up some zip codes to use it though and make sure to choose the package option even if it's a padded envelope. There is an option to input the weights as metric as well.