May one Daven with his hands in his pocket?
One is required to stand [before G-d] during the prayer [of Shemoneh Esrei] like a servant stands before his master, in a way of awe, fear, and trepidation. Likewise, one is not to place his hands on his loins, as this is a form of arrogance. [Some understand from this Halacha that it comes to negate the placing of one’s hands in his pockets during Shemoneh Esrei, as it is not a dignified manner in which a servant stands before his master, and likewise often entails placing one’s hands by his loins. Accordingly, even placing the hands in the pockets of a short winter jacket would be negated. Nonetheless, if one’s hands are cold and it disturbs the person’s concentration, then he may enter his hands into his pockets for the sake of being able to concentrate on his prayer.]
 Admur 95:4
 Admur ibid; Michaber 95:3; Rambam Tefila 5:4; Hagahos Maimanis Tefila ibid Vav
 Admur ibid; Michaber ibid; Rambam ibid based on Brachos 24b; Or Zarua Tefila 100
 Although I have found no explicit source anywhere stating that one may or should not Daven with his hands in his pockets, practically, so is commonly understood by people, and many Rabbanim, and the reason is seemingly based on the above. Now, although not all pockets entail resting the hands by the loins [i.e. hip/thigh], such as the pockets of a winter jacket which rest by one’s abdomen, nevertheless, since in most likelihood one would not choose to stand in this method upon seeing a high dignitary, therefore it should not be done. Vetzaruch Iyun, as in today’s western society, I am unaware of any formal hand position that is kept when meeting with high profile individuals, and there seems to be no negation of having one’s hands by the thigh or in his pocket! On the contrary, in the army it is protocol for the hand to be kept by the sides of the thigh [i.e. loins?] and it is common for servants and butlers to cross their hands onto each other and position them under the loins upon speaking to their master. It is hence not understood why this position would be considered one of arrogance, and one that is unbefitting before a king. Seemingly then, one must say that the intent of the Shulchan Aruch which negates resting the hands by the loins, is not negating resting the hands by the thighs, but rather against bending the hands onto one’s actual loins. This is known as the akimbo position, in which the palms rest on the hips with the elbows flexed outward, bowed away from the body. This indeed is a haughty position, which expresses a body language of impatience and arrogance. Accordingly, placing one’s hands in one’s pockets does not transgress the above dictum against resting the hands by the loins, even if one’s hands end up resting on one’s thighs. Nonetheless, regarding the former aspect of appearance before a king, indeed common army protocol for generations is not to allow soldiers to put their hands in their pockets at any time, which would help boost the argument that placing your hands in your pockets is not considered a respectful form of body language and hence should not be done, whether by coat or pants pockets. Vetzaruch Iyun.
 Pashut, as first and foremost one is required to concentrate on his prayer, and likewise when one does so due to the cold there is no haughtiness involved. [See Beir Moshe 4:39; Piskeiy Teshuvos 91:5]