Your bike is a Colson and it is a nice find. The serial number stamped in the frame’s crank hanger may help date the build of the frame. The bike, as is - as built, asks a number of forensic questions as the mix of parts spans two or three years making it hard to determine the exact date and the correct full original build.
The frame is the short wheelbase no-tank “rainbow” double bar roadster frame that Colson introduced probably in late 1937 and continued to build at least through 1940.
The top tubes are located closer together than the similar version that was designed to take the Colson three-rib tank and its variants. The chain guard, the chain ring, and the fenders are all 1937 pattern parts and they were all redesigned for 1938. As a secondary, retail branded bike those parts could have been used from surplus for a while after 1937 to clear the shelves.
Another 1937 to 1938 change is the design of the forged fork, 1938 forks were improved with a stiffening ridge or peak in the crown, 1937 forks do not have this ridge and have smooth shoulders which it looks like your bike has. (hard to be sure from the photos.) Again, the transition from one fork to the other was not overnight and their use probably overlapped for a while.
The waterfall truss rod fork design also dates to 1937 (1936 for Colson Commanders) when it was used on deluxe bikes. In 1938 its use trickled down to mid level models as well. It is a myth that the slotted waterfall truss rod fork was specifically used on bikes with waterfall badges. It was easier to produce all the forks that way and in reality very few were originally equipped with waterfall badges. The waterfall badge has been repopped many times and is often added to bikes that also have a standard head badge. While there is no concrete evidence, one way or the other, many believe that bikes were not produced with two head badges and that if a bike has a standard head badge, or the frame has head badge holes, it did not originally have a waterfall badge.
Another interesting piece on this bike is the handlebar mounted horn button. Since this bike could not have come with a tank which could have held a horn and the button for it, it has the handlebar mounted button which signifies at one time it likely had a Delta hornlight and battery tube (Offered by the factory) or something similar. These parts are also typical for 1937 and were not used much later than that
So far, this all adds up to the bike being a 1937 model. On the 1938 side is the stem which is shown prominently in 1938 literature but not anywhere in the 1937 literature. Since it is a stem predominantly used by Colson it is likely original to the bike. The hole in the rear fender is for the tray of a Delta “Mouselite”(small in size, high in price) which was used in 1937 and 1938.
Putting all of the above together I would guess this bike was built in very late 1937 or during 1938 in which case it was absorbing parts that were being cleared from inventory. The nature of the bike’s build with the hole in the rear fender and the horn button on the bars suggest that it was originally a deluxe, unequipped model. These were popular at the time as they typically had many of the features and paint of the top of the line models but without all the extra bling for a more sophisticated and understated look.
As to the waterfall badge, I tend to believe that bikes were not double badged (the known Colson catalogs do not show double badged bikes) but ultimately there can be no definitive proof to back up that position (try to prove a negative) and there is too much time past to set proof on current examples with both.
And, I would not recover that seat. It is in marginal shape but it still has integrity and is likely original to the bike. There is no way to duplicate the blocked form and the stitching of that type of seat without special and heavy equipment. You could refinish the carriage and find a replacement top that no longer has a cover (plenty of those around) and then nothing original would be harmed by covering the bare pan to your taste.