I have an environment with a 2012 R2 RDS server farm consisting of:

RDGW - Gateway, Broker, RDWeb

RDS01, RDS02, RDS03 - Three RDS Session hosts

All users utilize RDWeb to connect to the farm. They navigate to rds.companyname.com and the RDS gateway load balances connections. 

We have a problem, in that there are about 75 old thin clients that are running Windows Embedded 6.0 and do not support a TS gateway. So, what can we do? I was going to configure old school round robin DNS, make an A record of rds for each of the three RDS session host IP's. I never entirely understood how RR DNS worked, is it entirely random? Is this the only solution I have for the old thin clients? What are some problems I might run in to? Purchasing new thin clients is not an option. 

Also, I know that we are never suppose to use RDP for 2012 anymore, and are only suppose to use RDWeb. But, let's say we buy some new thin clients that support RDP 8.1. Can we configured RDP connection to use the RD Gateway? When I try to use RDP on a desktop and I enter the gateway under advanced, and then the RDGW server name under comptuername, it tries logging me directly in to the gateway and does not send me to a session host. 

IMO your first idea about RR DNS is the better.

An example on how it work. (from https://technet.microsoft.com/en-us/library/cc787484(v=ws.10).aspx)

Example: Round-robin rotation

A forward lookup-type query (for all A RRs that match a DNS domain name) is made for a multihomed computer (multihomed.example.microsoft.com) that has three IP addresses. Separate A RRs are used to map the host's name to each of these IP addresses in the zone. In the stored example.microsoft.com zone, the RRs appear in this fixed order:

multihomed   IN  A  10.0.0.1

multihomed   IN  A  10.0.0.2

multihomed   IN  A  10.0.0.3

The first DNS client that queries the server to resolve this host's name receives the list in default order. When a second client sends a subsequent query to resolve this name, the list is rotated as follows:

multihomed   IN  A  10.0.0.2

multihomed   IN  A  10.0.0.3

multihomed   IN  A  10.0.0.1