Forza Horizon

There are 8 BMWs on the disc, and one available as a free sample car (the M3 GTR in the April TopGear pack). For the 10th BMW, it's best to buy the November Bondurant pack, since it includes a number of other cars required for the other manufacturer-specific achievements (although there is also a BMW M135i in the March Meguiar's pack).

You need to earn at least one medal in 10 different BMW cars. Press up on the D-pad to see the requirements for the medals.

Beware, although some cars are free to download, they still need to be purchased in game with either in-game credits or real money (MS Points), but that is the case for every car.

Unicorn cars
I do not include "unicorn" cars as free as you need to earn them and they are extremely rare, so most gamers will not have access to them.

Barn discovery cars
Barn discovery cars are available in the main game, but you have to progress through the story and multiplayer, to have them appearing on your map. Then you have to find them in the barn (wrecked). You have to wait until they are fixed before you can use them. There are 9 Barn discovery cars.
* 1964 Aston Martin DB5
* 1958 Aston Martin DBR1
* 1981 BMW M1
* 1992 Bugatti EB110 SS
* 1957 Ferrari 250 Testa Rossa
* 1956 Jaguar D-Type
* 1954 Mercedes 300SL Gullwing Coupe
* 1971 Plymouth Cuda 426 HEMI
* 1965 Shelby Cobra Daytona Coupe

Loyalty cars
To get your loyalty cars you need at least a save file from either FM3 or FM4. Depending on your level, you get those cars:
* 2011 MINI Cooper S (Level 1)
* 2011 Citroen DS3 Racing (Level 5)
* 2012 Dodge Charger SRT8 (Level 10)
* 1969 Chevrolet Camaro SS (Level 15)
* 2008 BMW M3 E92 (Level 20)
* 2012 Jaguar XKR-S (Level 30)
* 2009 Gumpert Apollo S (Level 40)
* 2012 Lamborghini Aventador LP700-4 (Level 50)

Forza Rewards Program
https://rewards.forzamotorsport.net/
Depending on your tier, you get rewards monthly. Redeem them on the site and they will be deliverer in your game within 4 hours. The rewards can be money, cars, tokens,...

Available DLC Packs
* October Car Pack (1957 Chevrolet Bel Air - FREE)
* November Bondurant Car pack (2012 Jeep Wrangler Rubicon - FREE)
* Season pass (2006 Lamborghini Miura Concepts - FREE)
* December IGN Car Pack (1971 AMC Javelin AMX - FREE)
* Rally expansion pack NOT FREE - NO FREE CARS
* January Recaro Car Pack (1995 Ford Mustang Cobra R - FREE)
* Honda Challenge Car Pack - FREE pack, includes 3 free Honda Cars (2013 Civic Si Coupe - 1986 Honda Civic Si - 2013 Honda HDP Fit - FREE)
* February Jalopnik Car Pack (1966 Ford Country Squire - FREE)
* March Meguiar's Car Pack (1998 Nissan R390 - FREE)
* April TopGear Car Pack (2002 BMW M3 GTR - FREE)

Complete List
* 1973 BMW 2002 Turbo (main game)
* 1981 BMW M1 (Barn discovery - main game)
* 1991 BMW M3 (main game)
* 2002 BMW M3 GTR (FREE DLC)
* 2008 BMW M3 (Loyalty car)
* 2010 BMW M3 GTS (DLC)
* 2011 BMW 1 Series M Coupe (main game)
* 2012 BMW Z4 sDrive28i (main game)
* 2012 BMW M5 (main game)
* 2013 BMW M6 Coupe (main game)
* 2013 BMW M135i (DLC)

Summary: 6 cars (main game) + 1 Barn discovery (main game) + 2 cars (non free DLC) + 1 car (free DLC) + 1 Loyalty Car

I suggest you buy the November Bondurant Car Pack as you need to buy it anyway if you want to unlock the next achievement: