Several crucial issues are discussed in the design of cryogenic cooling system for high field magnets. This study is mainly motivated by our ongoing program to develop a 21 T Fourier Transform Ion Cyclotron Resonance Mass Spectrometer (FT-ICR MS). The magnets of this system will be built horizontally to accomplish the requirement of user friendliness and reliability, and the replenishment of cryogen will not be necessary by a closed-loop cooling concept. The initial cool-down and safety are basically considered in this paper. The effects of the helium II volume and the gap distance of the weight load relief valve (or safety valve) on the cool-down time and temperature rising during an off-normal state are discussed. The total amount of cryogenic cooling loads and the required helium flow rate during cool-down are also estimated by a relevant heat transfer analysis. The temperatures of cryogen-free radiation shield are finally determined from the refrigeration power of a cryocooler and the total cryogenic loads.