Is the problem you are describing when you are decelerating?
When you are slowing and you push on the lever do you hear things whirring?
Your pic shows snow, is this concurrent with a temp drop?
Touching second gear speeds up the input shaft and makes the work of the first gear synchronizer much easier.
If I understand the scenario properly It sounds to me like worn synchros or to heavy or contaminated gear oil. Or perhaps a clutch not disengaging completely.Does it go into gear OK while standing still?
Since it improves with driving(temp) I would try fresh gear oil appropriate for your climate.