True, the plant is not going to utilize the nutrients if they are dormant--- and most things are dormant in Amarillo this time of year. I would certainly avoid application to frozen soils. It is a common practice in north central Texas to apply liquid UAN 32% N or 28%N to winter grains (cool-season grasses ) prior to breaking dormancy. The cool temps help reduce volatilization and plant burn. Fertilization on ryegrass overseeds is similar.
Early application of ferts to warm-season grasses are subject to premature leaching, degradation and denitrification during extremely wet conditions ( probably not a problem in Amarillo). Best efficiency will occur if plants are growing. Warnings of spring diseases is not a big issue in arid Amarillo.
To specifically address your question: we have made liquid winter apps on bermuda in the winter while soil temps were in the low 40's, but it was on properties that were new to care and had extreme fertility problems. They were done in an effort to "jump start" the recovery and spread-out workload. We will begin fertilizing ryegrass overseed ballfields next week with soil temps in the 40's---but will be using granular controlled release.