What are those white things on the windshield of most citation jets? Does it have to do with rain?
Those are ducts that form the ice and rain protection system for the windshield. That is a vague answer because the precise answer depends on which particular type you look at. The main thing you see is the shroud for ducting air for either anti-ice or rain removal.
Depending on the specific aircraft type, the ice and rain protection systems for the windshield may include one or more of:
- Hot engine bleed air for windshield Anti-Icing and rain removal
- Application system for alcohol De-Icing (left hand pilot side only)
- Movable doors for rain removal
- Pressurized (non heated) forced air rain removal system
The first three systems listed above are found on most if not all CE-500 (500/550/560) and CE-525 (M2, CJ, CJ1, CJ2, CJ3) variants (except the CJ4). The last item listed above is found on the CE-560XL type. Other types may also feature one of these systems, but I cannot speak to that with any authority.
The model in your picture is a Citation CE525 M2. I am not familiar with the M2 variant, but I believe it is representative of most CE525 (CitationJet) models up through the CJ3, but not including the CJ4. The CJ4 has an electrically heated windshield with rain repellent applied to the glass and does not have any of the above listed systems.
The main component visible in your photo above is is the shroud that ducts the the engine bleed air to the windscreen. This air is cooled and temperature controlled so as to be at a safe temperature to be applied to the laminated plastic windscreen in flight conditions. This is hot enough that extended ground use could soften or even melt a hole in the windscreen.
My training materials include the following system description which is applicable to most variants of the CE-500 and CE-525 types:
Windshield anti-ice is primarily accomplished by using bleed air to warm both front windscreen exteriors. The air comes out of nozzles within a shroud at the base of each windscreen. A backup alcohol system is provided for the left side if needed.
The Citation Excel CE-560XL type has a visually similar system. However, this system only provides low pressure air for rain removal. This air is ducted from the nose avionics compartment and pressurized by a fan. This air is not heated by the engines. If the avionics compartment builds up excessive heat (such as in extended ground operations) this same system is used to exhaust air from the avionics compartment for cooling.
If you have a look here you will note that they are the outlets for the pneumatic rain-protection-system.
 FAA. (2018). Aviation Maintenance Technician Handbook—Airframe Volume 2 (Chapter 15). Federal Aviation Admenstration.