For a lot of feelings it looks clear to me that a thought preceded it. Like when I think of the possibility of war I get afraid. But imagine the case when it is very cold, is the feeling of having cold preceded by the thought that it is cold or could you feel cold without thinking about it?
The "quick" answer is no. However, because you used the word "every feeling", it will take only one feeling without thought, to negate the premise.
Typically, thinking is a capability associated with "higher intelligence" forms. However, "lower intelligence" forms do have feelings, even though they are incapable of thinking, therefore, there is "feeling without thinking."
I'm going to say that this depends on what definition of "thought" you want to adhere to. Conscious thought or unconscious thought? Certainly every feeling or action taken by a human is preceded by some function of the brain (and/or reflex mechanisms, muscle memory, etc).
Is every feeling preceded by a conscious thought? No. Is there an unconscious function happening between a stimulus and a resultant feeling? Yes, and this is also sometimes followed by a conscious thought which can also precede the feeling but may happen after the feeling has been triggered.
To use your example of feeling afraid:
If a bear jumps out in your path and growls at you, you will very likely feel afraid faster than you can consciously think about your situation. However, as soon as you are able to gather yourself (assuming you do) you may also begin to have conscious thoughts about this event which lead to feelings.
Some feelings and reactions, either through repetition or other means, can become learned and automatic. Like a child learning to walk they will think about every step until eventually they can walk without consciously processing their every move. If you are able to have a single feeling as automatically as you can walk, then your answer is no, every feeling is not required to be preceded by a conscious thought.
From a point of view like that of theories of emotion like those of James and Lange, especially as elaborated in Antonio Damasio's somatic marker theory, it is more likely that a thought is sandwiched between the two halves of every emotion.
In those theories, emotions arise physiologically before the thoughts associated with them, but they are then evaluated in terms of experience before becoming actual feelings. That evaluation is a thought, one way or the other, even if it is often fleeting or unconscious.
The same physiological reaction might become fear, exhilaration, anger or passion, depending on the thought that shapes it. But the thought would not occur unless some emotion were already in the process of arising.
Damasio's evidence for this is that he observes those deprived of emotional reactions by brain damage often lose the ability to apply logic to everyday situations, even if their actual logic is unimpaired. His theory is that without the incipient emotion, logic often does not kick in and do its job of helping us make decisions.
For your example of cold, your body might actually start preparing to shiver, or raise gooseflesh to conserve body heat. Then your mind might have to decide whether it is cold, scared, or filled with anticipation before you actually feel cold. If you decide you are not actually cold, that incipient shiver might be transformed into something quite different, like a lurch out of the way, or a laugh.